CN109902414B

CN109902414B - Ultralow-frequency high-damping vibration isolator, parameter determination method and device and track

Info

Publication number: CN109902414B
Application number: CN201910174043.4A
Authority: CN
Inventors: 韦凯; 赵泽明; 王平; 李怀龙; 杜香刚; 肖俊恒; 刘伟斌; 施成; 王绍华; 欧灵畅; 肖杰灵; 陈嵘; 徐井芒; 何庆
Original assignee: Southwest Jiaotong University; China Academy of Railway Sciences Corp Ltd CARS; Railway Engineering Research Institute of CARS
Current assignee: Southwest Jiaotong University; China Academy of Railway Sciences Corp Ltd CARS; Railway Engineering Research Institute of CARS
Priority date: 2019-03-07
Filing date: 2019-03-07
Publication date: 2021-02-05
Anticipated expiration: 2039-03-07
Also published as: CN109902414A

Abstract

The ultra-low frequency high-damping vibration isolator, the parameter determining method and device and the rail provided by the embodiment of the application relate to the field of rail transit vibration attenuation; the vibration isolator comprises: the positive stiffness elastic part, the negative stiffness elastic part and the controllable damping part determine the positive stiffness coefficient of the vibration isolator according to the maximum deformation of the vibration isolator, acquire the initial index value of the negative stiffness elastic part, further establish a relational expression between the stiffness coefficient of the vibration isolator and the negative stiffness coefficient of the negative stiffness elastic part, and determine the negative stiffness coefficient. And determining the controllable damping force according to a relational expression between the support reaction force borne by the vibration isolator and the controllable damping force of the controllable damping part. And then can make the isolator all have good effect in reducing natural frequency and restraining vibration, and when the isolator was applied to among the track system, can fine reduction train that moves on the track brought the vibration harm.

Description

Ultralow-frequency high-damping vibration isolator, parameter determination method and device and track

Technical Field

The application relates to the field of rail transit vibration reduction, in particular to an ultralow-frequency high-damping vibration isolator, a parameter determination method and device and a rail.

Background

Along with the development of rail transit, more and more cities are provided with rail transit means such as subways and light rails, and the life of people is facilitated. However, when the train travels on the track, it causes environmental vibrations that affect the health of the passengers. The vibration of the environment is related to the structure of the track, and the steel spring floating plate track in the prior art is the track with the best damping effect and has a wider damping frequency band. However, the natural frequency of the steel spring floating plate rail is relatively high, so that the resonance phenomenon is easy to generate, and when the resonance occurs, the damage to the environment is larger due to large vibration amplitude.

Disclosure of Invention

The embodiment of the application aims to provide an ultralow-frequency high-damping vibration isolator, a parameter determining method, a parameter determining device and a track, and can solve the problems that the vibration amplitude of a floating slab track is too large and the vibration damping effect is not obvious.

In a first aspect, an embodiment of the present application provides a method for determining a parameter of a vibration isolator, where the vibration isolator includes: a positive stiffness elastic member, a negative stiffness elastic member and a controllable damping member;

obtaining the positive stiffness coefficient according to the preset maximum deformation of the vibration isolator in the vertical vibration direction;

acquiring the initial length of the negative stiffness elastic part, the installation number of the negative stiffness elastic part in the vibration isolator and the length of the negative stiffness elastic part when the negative stiffness elastic part is vertical to the positive stiffness elastic part;

constructing a first relation determined by the stiffness coefficient of the vibration isolator, the negative stiffness coefficient of the negative stiffness elastic part, the positive stiffness coefficient, the initial length, the installation number and the length; the value of the stiffness coefficient of the vibration isolator is required to meet the preset maximum deformation quantity of the vibration isolator in the vertical vibration direction, wherein the maximum deformation quantity of the vibration isolator in the vertical vibration direction is smaller than the preset maximum deformation quantity;

and when the stiffness coefficient of the vibration isolator takes a minimum value within a value-taking range, calculating the negative stiffness coefficient according to the first relational expression.

In the embodiment of the application, the vibration isolator comprises the positive stiffness elastic part, the negative stiffness elastic part and the controllable damping part, the positive stiffness elastic part and the negative stiffness elastic part are matched with each other, so that the natural frequency of the floating slab track can be reduced, the vibration isolation range is further improved, the elastic coefficient of the negative stiffness elastic part is determined through the steps in the method, the vibration isolation range of the vibration isolator can be improved as far as possible while the train running on the floating slab track can be safely driven, and the vibration isolation effect is also improved equivalently. And because the controllable damping part is also arranged in the vibration isolator, the vibration can be inhibited. Therefore, the vibration effect caused by the floating slab track can be well reduced by mutually matching the positive stiffness elastic piece, the negative stiffness elastic piece and the controllable damping piece.

Optionally, constructing a first relation between the stiffness coefficient of the vibration isolator and the negative stiffness coefficient, the positive stiffness coefficient, the initial length, the number of the mounts, and the length includes:

acquiring a second relational expression between the force of the vibration isolator in the vertical vibration direction and the deformation of the vibration isolator in the vertical vibration direction, wherein in the second relational expression, the force of the vibration isolator in the vertical vibration direction is positively correlated with the positive stiffness coefficient of the positive stiffness elastic member and the damping force of the controllable damping member, and the force of the vibration isolator in the vertical vibration direction is also correlated with the initial length, the installation number, the length and the negative stiffness coefficient;

and obtaining the first relational expression by differentiating the deformation quantity in the second relational expression.

The second relational expression that earlier carries out stress analysis to the isolator and determine in this application, whether the orbital bearing capacity of reaction floating slab can be audio-visual satisfies the needs, and then makes the negative stiffness coefficient who calculates through first relational expression more scientific.

Optionally, the second relation is:

wherein F is the force applied to the vibration isolator in the vertical vibration direction, F₀Is the initial deflection force, F, of the vibration isolator_dFor damping forces, Z_cDimensionless as coulomb frictionHysteresis, X being the distance by which the positive stiffness member shortens,

for the speed of shortening of said positive stiffness member, k_vThe positive stiffness coefficient is determined by the preset maximum deformation amount x, L is the length of the negative stiffness elastic member when the negative stiffness elastic member is perpendicular to the positive stiffness elastic member, L is the initial length of the negative stiffness elastic member, n is the number of the negative stiffness elastic members, and k is the number of the negative stiffness elastic members_hThe negative stiffness coefficient.

In the embodiment of the application, it can be seen from the expression of the second relational expression that dimensionless hysteresis quantities of the initial polarization force and the coulomb friction force of the vibration isolator are also considered when the force of the vibration isolator in the vertical vibration direction is calculated, so that the calculated force of the vibration isolator in the vertical vibration direction is more accurate.

Optionally, the second relation is obtained by:

establishing a third relation: f ═ F_v+F_i；

Wherein, F_vIs the sum of the forces applied to the positive stiffness elastic member and the controllable damping member in the vertical vibration direction, F_iThe component force of the negative stiffness elastic piece in the projection direction along the shortening direction of the positive stiffness piece;

establishing a fourth relation: f ═ F_v+F_hsinα；

Wherein, F_hIs the force applied to the negative stiffness elastic member, and alpha is the complementary angle of the acute included angle between the negative stiffness elastic member and the positive stiffness elastic member,

establishing a fifth relation:

and obtaining the second relational expression according to the third relational expression, the fourth relational expression and the fifth relational expression.

In the embodiment of the application, the second relational expression can be obtained through mutual iteration of the third relational expression, the fourth relational expression and the fifth relational expression, so that the stress condition of each elastic part when the vibration isolator vibrates in the vertical vibration direction can be obtained, and the vibration attenuation effect of the vibration isolator can be conveniently analyzed.

Optionally, after calculating the negative stiffness coefficient according to the first relation, the method further comprises:

judging whether the negative stiffness coefficient is larger than the stiffness coefficient of the vibration isolator or not;

if the negative stiffness coefficient is larger than the stiffness coefficient of the vibration isolator, reducing the range of the stiffness coefficient of the vibration isolator from a minimum value to a preset interval, and determining a new range of the stiffness coefficient of the vibration isolator;

and when the new minimum value of the stiffness coefficient of the vibration isolator is within the range of the available value, calculating the negative stiffness coefficient according to the first relational expression.

In the embodiment of the present application, when the negative stiffness coefficient is obtained through the first relational expression, the negative stiffness coefficient needs to be determined so that the value of the negative stiffness coefficient is reasonable, and the vibration damping effect of the vibration isolator is better.

Optionally, the first relation is:

wherein k is_vThe positive stiffness coefficient is determined by the preset maximum deformation amount x, L is the length of the negative stiffness elastic member when the negative stiffness elastic member is perpendicular to the positive stiffness elastic member, L is the initial length of the negative stiffness elastic member, n is the number of the negative stiffness elastic members, k is the maximum deformation amount x, n is the initial length of the negative stiffness elastic member, n is the number of the negative stiffness elastic members, k is the maximum deformation amount x, and_hand K is the stiffness coefficient of the vibration isolator.

In the embodiment of the application, the relation between the stiffness coefficient of the vibration isolator and the positive stiffness coefficient and the negative stiffness coefficient can be seen through the first relational expression, so that reasonable values can be conveniently taken when the stiffness coefficient and the positive stiffness coefficient of the vibration isolator are determined, and the negative stiffness coefficient of the vibration isolator can be determined more quickly.

Optionally, the method further comprises:

acquiring the number of the vibration isolators below the floating plate and the support reaction force applied to the vibration isolators below the floating plate;

and determining the damping force parameters of the controllable damping part according to the number of the vibration isolators and the bearing reaction force to which the vibration isolators are subjected.

In this application embodiment, can determine the damping force parameter of controllable damping piece through above-mentioned mode, can restrain the vibration through setting up reasonable damping force parameter, the floating plate rail stage property of being convenient for has better damping effect.

Optionally, the damping force parameter of the controllable damping member is determined according to the number of vibration isolators, the reaction force to which the vibration isolators are subjected, and a sixth relation:

wherein Z is_s(x_iT) is the displacement of the floating plate in vertical vibration at the moment t,

is to Z_s(x_iT) derivation of the displacement, i.e. the velocity of the floating plate vibrating vertically at time t, N being the number of vibration isolators below the floating plate, F_ssjIs the bearing reaction force to which the vibration isolator is subjected.

In a second aspect, the present application provides a parameter determination apparatus for a vibration isolator, the vibration isolator comprising: a positive stiffness elastic member, a negative stiffness elastic member and a controllable damping member; the device comprises:

and the first data acquisition module is used for acquiring the stiffness coefficient according to the preset maximum deformation of the vibration isolator in the vertical vibration direction.

And the second data acquisition module is used for acquiring the initial length of the negative stiffness elastic part, the installation number of the negative stiffness elastic part in the vibration isolator and the length of the negative stiffness elastic part when the negative stiffness elastic part is vertical to the positive stiffness elastic part.

The construction module is used for constructing a first relational expression determined by the stiffness coefficient of the vibration isolator and the negative stiffness coefficient, the positive stiffness coefficient, the initial length, the installation number and the length of the negative stiffness elastic part; and the value of the stiffness coefficient of the vibration isolator is required to meet the condition that the maximum deformation of the vibration isolator in the vertical vibration direction is smaller than a preset maximum deformation.

And the parameter determination module is used for calculating the negative stiffness coefficient according to the first relational expression when the stiffness coefficient of the vibration isolator takes a minimum value within a value-taking range.

In a third aspect, the present application further provides an ultra-low frequency high damping vibration isolator, including: a positive stiffness elastic member, a negative stiffness elastic member and a controllable damping member; wherein the negative stiffness coefficient of the negative stiffness elastic member and the damping force of the controllable damping member are determined by steps of any of the methods of the first aspect.

In a fourth aspect, the present application further provides a track, which includes a steel rail, a floating slab and the ultra-low frequency high damping vibration isolator described in the third aspect, wherein the steel rail is disposed above the floating slab and connected to the floating slab through a fastener, and the ultra-low frequency high damping vibration isolator is disposed below the floating slab.

In a fifth aspect, the present application further provides a readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of any of the methods in the first aspect.

In order to make the aforementioned objects, features and advantages of the present application more comprehensible, embodiments accompanied with figures are described in detail below.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained from the drawings without inventive effort.

Fig. 1 is a schematic flow chart of a method for determining vibration isolator parameters according to an embodiment of the present disclosure;

fig. 2 is a schematic structural diagram of a vibration isolator according to an embodiment of the present application;

fig. 3 is a schematic structural view of another vibration isolator provided in an embodiment of the present application;

fig. 4 is a schematic flow chart illustrating a further method for determining vibration isolator parameters according to an embodiment of the present disclosure;

fig. 5 is a schematic flow chart illustrating a method for determining vibration isolator parameters according to an embodiment of the present disclosure;

fig. 6 is a schematic flow chart illustrating a further method for determining vibration isolator parameters according to an embodiment of the present disclosure;

fig. 7 is a schematic flow chart illustrating a further method for determining vibration isolator parameters according to an embodiment of the present disclosure;

figure 8 is a schematic diagram comparing the time domain and the frequency domain of the bearing reaction force on a conventional steel spring and a quasi-zero stiffness vibration isolator provided by the embodiments of the present application;

FIG. 9 is a schematic diagram of a comparison between time domain and frequency domain of the reaction force of a conventional steel spring and a magnetorheological damping vibration isolator provided in an embodiment of the present application;

figure 10 is a schematic diagram comparing the time domain and the frequency domain of the support reaction force of a conventional steel spring and an ultra-low frequency high damping nonlinear vibration isolator provided by the embodiment of the application;

figure 11 is a schematic comparison of acceleration in time and frequency domain for a conventional steel spring and quasi-zero stiffness isolator as provided in embodiments of the present application;

FIG. 12 is a schematic diagram illustrating acceleration of a conventional steel spring and a magnetorheological damping vibration isolator in comparison in time and frequency domains according to an embodiment of the present application;

figure 13 is a schematic diagram comparing the acceleration of a conventional steel spring with the acceleration of an ultra-low frequency high damping nonlinear vibration isolator in time domain and frequency domain according to an embodiment of the present application;

fig. 14 is a functional block diagram of a vibration isolator parameter determination apparatus according to an embodiment of the present application.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some embodiments of the present application, but not all embodiments. The components of the embodiments of the present application, generally described and illustrated in the figures herein, can be arranged and designed in a wide variety of different configurations.

It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.

In the description of the present application, it is further noted that, unless expressly stated or limited otherwise, the terms "disposed," "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; the elastic pieces can be directly connected or indirectly connected through an intermediate medium, and the two elastic pieces can be communicated with each other. The specific meaning of the above terms in the present application can be understood in a specific case by those of ordinary skill in the art.

Referring to fig. 1, an embodiment of the present application provides a flowchart of a method for determining a parameter of a vibration isolator, where the vibration isolator may include: a positive stiffness spring, a negative stiffness spring, and a controllable damping member.

The vibration isolator in the embodiment of the application can be applied to the floating slab track and used for reducing the vibration of the floating slab track caused by the movement process of a train on the floating slab track. The positive stiffness elastomer in the isolator in this application is used to provide the isolator with a certain stiffnessThe coefficient is that the vibration isolator can support enough weight, the negative stiffness elastic part and the positive stiffness elastic part can be matched in a parallel connection mode, and the natural frequency of the floating slab track can be reduced. In the floating plate orbit, the excitation frequency is only higher than that of the floating plate orbit

When the natural frequency is lower than the preset value, the floating slab track can play a good vibration isolation effect, so that the natural frequency of the floating slab track is reduced, which is equivalent to the increase of the vibration isolation range of the floating slab track. Meanwhile, the vibration isolator also comprises a controllable damping part which is used for reducing the deformation amount of the floating plate in the vertical vibration direction, so that the downward regulation amount of the supporting rigidity of the floating plate can be increased, and the vibration of the floating plate track caused at the natural frequency can be restrained, thereby further improving the vibration isolation efficiency of the floating plate track. The following detailed description will be made in conjunction with specific embodiments, all of which are exemplified by the application of the vibration isolator to the floating plate rail. In order to facilitate understanding of the structure of the vibration isolator, the embodiment of the application provides a structural schematic diagram of the vibration isolator, as shown in fig. 2. The schematic of the structure for placing the vibration isolator in the floating slab track is shown in figure 3.

In fig. 2, it can be seen that the positive stiffness elastic member and the negative stiffness elastic member are both steel springs, and there are two negative stiffness elastic members in fig. 2, and the two negative stiffness elastic members are symmetrically arranged on two sides of the positive stiffness elastic member. In fig. 3 it can be seen that the vibration isolators are placed on the foundation, i.e. the foundation of the floating slab track, and it can be seen that there are a plurality of identical vibration isolators under one floating slab, and that the plurality of vibration isolators are arranged at a certain distance. A steel rail fastener is arranged above the floating plate, one end of the steel rail fastener is connected with the floating plate, and the other end of the steel rail fastener is connected with the track. It should be noted that fig. 2 and 3 are only schematic diagrams provided for facilitating understanding of the vibration isolator provided in the embodiment of the present application, and do not limit the vibration isolator in the embodiment of the present application.

Step S110: and obtaining the positive stiffness coefficient according to the preset maximum deformation of the vibration isolator in the vertical vibration direction.

Because the train running on the floating slab track has larger mass, the safety of the normal running of the train is ensured; the overall structure of the floating slab track should have certain rigidity, so that accidents caused by the fact that the track is soft in the running process of a train are avoided. The preset maximum deformation of the floating slab track in the vertical vibration direction can be determined according to actual requirements in the actual application process, and the preset maximum deformation of the vibration isolator in the vertical vibration direction can be 3 mm. And then determining the positive stiffness coefficient of the positive stiffness elastic member.

Step S120: obtaining the initial length of the negative stiffness elastic member, the number of the negative stiffness elastic members installed in the vibration isolator, and the length of the negative stiffness elastic member when the negative stiffness elastic member is perpendicular to the positive stiffness elastic member.

In the vibration isolator provided by the embodiment of the application, the negative stiffness elastic part and the positive stiffness elastic part can be arranged in parallel. The vibration isolator is arranged below the floating slab, and the installation space below the floating slab is limited. Therefore, in a specific embodiment, the initial length of the negative stiffness spring, and the number of negative stiffness springs may be determined according to the size of the space under the floating plate. When the vibration isolator is in the preset maximum deformation amount in the vertical vibration direction, the negative rigidity elastic part can be perpendicular to the positive rigidity elastic part, the mounting position of the negative rigidity elastic part can be determined at the moment, and then the length of the negative rigidity elastic part is obtained when the negative rigidity elastic part is perpendicular to the positive rigidity elastic part.

Step S130: constructing a first relation determined by the stiffness coefficient of the vibration isolator, the negative stiffness coefficient, the positive stiffness coefficient, the initial length, the installation number and the length; and the value of the stiffness coefficient of the vibration isolator is required to meet the preset maximum deformation of the vibration isolator in the vertical vibration direction, wherein the maximum deformation is smaller than the preset maximum deformation.

The first relational expression is a relational expression of the stiffness coefficient of the vibration isolator and the negative stiffness coefficient of the negative stiffness elastic member, and the unknown number in the first relational expression is the stiffness coefficient of the vibration isolator and the negative stiffness coefficient of the negative stiffness elastic member because the positive stiffness coefficient of the positive stiffness elastic member, the negative stiffness coefficient of the negative stiffness elastic member, the initial length of the negative stiffness elastic member, the number of the negative stiffness elastic members and the length of the negative stiffness elastic member when the negative stiffness elastic member is perpendicular to the positive stiffness elastic member are all obtained in the steps.

The first relation in the embodiment of the present application may be:

Step S140: and when the stiffness coefficient of the vibration isolator takes a minimum value within a value-taking range, calculating the negative stiffness coefficient according to the first relational expression.

When the isolator was applied to floating slab track, the rigidity coefficient of isolator should satisfy the driving safety driving demand of train, and then can determine the desirable value scope of the rigidity coefficient of isolator, in the desirable value scope of isolator rigidity coefficient, when the rigidity coefficient is less, floating slab track's natural frequency just lower this moment, the damping effect this moment just also is better. Therefore, when the value of the negative stiffness coefficient is determined, the value of the negative stiffness coefficient can be determined by taking a minimum value within the range of the acceptable value of the stiffness coefficient of the vibration isolator. For example, when the stiffness coefficient of the vibration isolator is preferably in the range of 9.00KN/mm to 15.00KN/mm, the negative stiffness coefficient of the negative stiffness spring in the vibration isolator can be determined by using the stiffness coefficient of the vibration isolator as 9.00 KN/mm.

In the embodiment of the application, the vibration isolator combines the positive stiffness elastic part, the negative stiffness elastic part and the controllable damping part, reduces the natural frequency through the matching of the positive stiffness elastic part and the negative stiffness elastic part, and inhibits the vibration through the controllable damping part, so that a good vibration reduction effect can be achieved. And the negative stiffness coefficient is determined by establishing a first relation between the overall stiffness coefficient of the vibration isolator and the negative stiffness coefficient of the negative stiffness elastic part, so that the vibration caused by train operation can be reduced as much as possible while the safe operation of the train is ensured.

Optionally, referring to fig. 4, in step S130, constructing a first relation between the stiffness coefficient of the vibration isolator and the negative stiffness coefficient, the positive stiffness coefficient, the initial length, the number of mounts, and the length, includes:

step S132: acquiring a second relational expression between the force of the vibration isolator in the vertical vibration direction and the deformation of the vibration isolator in the vertical vibration direction, wherein in the second relational expression, the force of the vibration isolator in the vertical vibration direction is positively correlated with the positive stiffness coefficient of the positive stiffness elastic member and the damping force of the controllable damping member, and the force of the vibration isolator in the vertical vibration direction is also correlated with the initial length, the installation number, the length and the negative stiffness coefficient;

step S134: and obtaining the first relational expression by differentiating the deformation quantity in the second relational expression.

That is, in the second relational expression, it is necessary to obtain the relationship between the force to which the vibration isolator is subjected and the amount of deformation of the vibration isolator. When the relation between the force borne by the vibration isolator and the deformation of the vibration isolator is obtained, stress analysis is carried out on the vibration isolator, one end, far away from the positive stiffness elastic part, of the negative stiffness elastic part is taken as a coordinate origin, a coordinate axis is established by a straight line perpendicular to the positive stiffness elastic part and penetrating through the coordinate origin, and the vertical vibration direction is taken as the positive direction. At the moment, the stress of the negative stiffness elastic part is distributed to the positive direction, and a relational expression between the total force of the vibration isolator in the positive direction and the deformation of the vibration isolator, namely a second relational expression, is established. In establishing the second relation, the initial biasing force of the vibration isolator and the dimensionless hysteresis quantity of the coulomb friction force of the vibration isolator are also considered.

In the embodiment of the application, the initial biasing force and the dimensionless hysteresis are independent of the deformation amount of the vibration isolator, and therefore, after the deformation amount in the second relational expression is derived, the first relational expression is the relational expression of the stiffness coefficient of the vibration isolator, the positive stiffness coefficient, the negative stiffness coefficient, the initial length of the negative stiffness elastic member, the installation number of the negative stiffness elastic member and the length of the negative stiffness elastic member when the negative stiffness elastic member is perpendicular to the positive stiffness elastic member.

In the embodiment of the present application, the second relation is:

wherein F is the force applied to the vibration isolator in the vertical vibration direction, F₀Is the initial deflection force, F, of the vibration isolator_dFor damping forces, Z_cIs the dimensionless hysteresis of the coulomb friction force, X is the shortened distance of the positive stiffness member,

Alternatively, referring to fig. 5, the second relation may be obtained by the following steps.

Step S1322: establishing a third relation: f ═ F_v+F_i；

Wherein, F_vIs the sum of the forces applied to the positive stiffness elastic member and the controllable damping member in the vertical vibration direction, F_iThe component force of the negative stiffness elastic piece in the projection direction along the shortening direction of the positive stiffness piece.

Step S1324: establishing a fourth relation: f ═ F_v+F_hsinα；

Wherein, among others,F_his the force applied to the negative stiffness elastic member, and alpha is the complementary angle of the acute included angle between the negative stiffness elastic member and the positive stiffness elastic member,

step S1326: establishing a fifth relation:

step S1328: and obtaining the second relational expression according to the third relational expression, the fourth relational expression and the fifth relational expression.

Of course, the order among step S1322, step S1324 and step S1328 may be changed, and when the method is executed, step S1324 may be executed first, step S1322 may be executed, and step S1328 may be executed last, or step S1328 may be executed first, step S1324 may be executed, and step S1322 may be executed last.

After the second relational expression is obtained, derivation is carried out on the deformation quantity in the second relational expression, and the first relational expression can be obtained.

Referring to fig. 6, in the embodiment of the present application, after obtaining the first relation in the above manner, the method further includes:

step S150: and judging whether the negative stiffness coefficient is larger than the stiffness coefficient of the vibration isolator.

Step S160: if the negative stiffness coefficient is larger than the stiffness coefficient of the vibration isolator, reducing the range of the stiffness coefficient of the vibration isolator from a minimum value to a preset interval, and determining a new range of the stiffness coefficient of the vibration isolator.

Step S170: and when the new minimum value of the stiffness coefficient of the vibration isolator is within the range of the available value, calculating the negative stiffness coefficient according to the first relational expression.

After determining the negative stiffness coefficient through the first relational expression, judging whether the negative stiffness coefficient meets the specification; for example, when the negative stiffness coefficient is calculated to be greater than the stiffness coefficient of the isolator, it is clearly not in compliance with the regulations. The stiffness coefficient of the vibration isolator taken by the vibration isolator is far smaller than the positive stiffness coefficient of the vibration isolator, so that the vibration attenuation effect is possibly not obvious. At the moment, the stiffness coefficient of the vibration isolator needs to be increased by a preset interval, and the negative stiffness coefficient of the elastic part with the negative stiffness is determined through the first relational expression again. The negative rigidity coefficient of the negative rigidity elastic element can meet the requirement. In other words, in the embodiment of the application, the negative stiffness coefficient is determined by continuously taking values within the desirable range of the stiffness coefficient of the vibration isolator. In a specific embodiment, when the negative stiffness coefficient is directly determined as 0, the stiffness coefficient of one vibration isolator can be calculated by substituting the first relational expression. The calculated stiffness coefficient can be used as the maximum value of the stiffness coefficient of the vibration isolator, and then the preset interval can be directly reduced from the maximum value in sequence until the vibration reduction effect of the vibration isolator reaches the best.

It should be noted here that theoretically, the smaller the stiffness coefficient of the vibration isolator is, the better the vibration damping effect is; however, in practical application, the model and parameters of the positive stiffness elastic element and the matching of the negative stiffness elastic element and the positive stiffness elastic element need to be considered. Therefore, in the actual application process, when the stiffness coefficient of the vibration isolator is determined, MATLAB simulation software can be used for simulating the vibration reduction effect of the vibration isolator at the moment, the range of the available value of the stiffness coefficient of the vibration isolator is changed by a preset interval again, the vibration reduction effect of the vibration isolator is simulated again, and the process is carried out until the stiffness coefficient corresponding to the vibration isolator with the best vibration reduction effect is found and the negative stiffness coefficient corresponding to the stiffness coefficient is found. The method includes the steps that 10 continuous stiffness coefficients are taken as examples to illustrate how to obtain stiffness coefficients corresponding to the vibration isolator with the best vibration reduction effect, and the stiffness coefficients are numbered as a first stiffness coefficient, a second stiffness coefficient … …, a ninth stiffness coefficient and a tenth stiffness coefficient in sequence; in the 10 consecutive stiffness coefficients, if the damping effects corresponding to the first stiffness coefficient to the sixth stiffness coefficient are sequentially increased, the damping effects corresponding to the sixth stiffness coefficient to the tenth stiffness coefficient are sequentially decreased, so that the sixth stiffness coefficient can be used as the stiffness coefficient corresponding to the vibration isolator with the best damping effect. If two stiffness coefficients with the same damping effect exist, if the damping effects corresponding to the first stiffness coefficient to the fifth stiffness coefficient are sequentially increased, the damping effects corresponding to the sixth stiffness coefficient to the tenth stiffness coefficient are sequentially decreased, and the damping effects corresponding to the fifth stiffness coefficient and the sixth stiffness coefficient are the same; at this time, the five stiffness coefficient or the sixth stiffness coefficient can be used as the stiffness coefficient corresponding to the vibration isolator with the best damping effect. Or a new interval can be reestablished by the fifth stiffness coefficient and the sixth stiffness coefficient, and the stiffness coefficients of the vibration isolators are increased according to the new interval in sequence.

For example, when the fifth stiffness coefficient reaches the sixth stiffness coefficient, a fifty-first stiffness coefficient, a fifty-second stiffness coefficient … …, a fifty-eighth stiffness coefficient, and a fifty-ninth stiffness coefficient are sequentially arranged at the same interval, and the stiffness coefficients corresponding to the vibration isolator with the best vibration damping effect are determined again according to the above method, which is not described again.

It should be noted that the preset interval in the embodiment of the present application may be selected according to actual requirements, and is not limited; for example, the predetermined interval may be 0.01 KN/mm; and at the moment, if the calculated negative stiffness coefficient does not meet the requirement of the stiffness coefficient of the vibration isolator, the stiffness coefficient of the vibration isolator is calculated again until the calculated negative stiffness coefficient meets the requirement, wherein the stiffness coefficient of the vibration isolator is 9.01 KN/mm.

Referring to fig. 7, in the embodiment of the present application, if the vibration isolator is used in the floating slab track, the damping force parameter of the controllable damping force can be determined by the following method:

step S210: and acquiring the number of the vibration isolators below the floating plate and the support reaction force to which the vibration isolators below the floating plate are subjected.

Vibration isolators are installed below the floating plates, and the number of the vibration isolators which can be installed is determined according to the size of the space below each floating plate. And a certain force is applied above the floating plate, so that the support reaction force borne by each vibration isolator can be determined. The force applied above the floating deck may be the maximum force that a single floating deck can withstand, determined by the maximum mass of the train running on the floating deck track. And the forces of a plurality of vibration isolators arranged below the same floating slab are almost the same. The magnitude of the reaction force experienced by each isolator can then be determined by determining the force above the floating plate.

Step S220: and determining the damping force parameters of the controllable damping part according to the number of the vibration isolators and the bearing reaction force to which the vibration isolators are subjected.

In the embodiment of the application, the support reaction force applied to the vibration isolator is positively correlated with the damping force parameter of the controllable damping member. After the force applied to the floating plate is determined, the supporting reaction force borne by each vibration isolator can be determined according to the number of the vibration isolators below the floating plate, and then the damping force parameter of the controllable damping part is determined.

When the damping force parameter of the controllable damping part is obtained, a third formula is required to be combined:

As can be seen from the third formula, the unknown quantity is only F_d(ii) a And F_dThe larger the value of (a), the better the suppression effect on the vibration. However, when F_dWill amplify the high-frequency vibration when the value of (2) is too large; thus, in determining F_dWhen the value of (A) is greater than (B), an F can be determined_dAnd in turn decrease F_dTo do so byThis determines the optimal F_d。

In the determination of F_dThe damping force parameter in the embodiment of the present application may be smaller than the damping force parameter in the magnetorheological vibration isolator because the negative stiffness elastic member is not added to the magnetorheological vibration isolator. Furthermore, the damping force parameter in the magnetorheological vibration isolator can be set to be the maximum damping force parameter of the application. And then sequentially determining the damping force parameters to finally determine the damping force parameters. Of course, the magnitude of each reduction may be determined as a practical matter.

It should be noted that when determining the damping force parameter in the magnetorheological vibration isolator, the damping force parameter should be under the same environment as the vibration isolator of the present application. For example, all are used in floating slab tracks and the number of magnetic fluid isolators under each floating slab is the same as the number of isolators of the present application and the positive stiffness coefficient in the positive stiffness elastomer is the same.

In the embodiment of the application, in the process of determining the parameters (the positive stiffness coefficient, the negative stiffness coefficient and the controllable damping force parameter) of the vibration isolator by the method, when the vibration damping effect of the vibration isolator is judged, the support reaction force on the floating plate and the acceleration of the floating plate can be monitored. That is, in the embodiment of the present application, the vibration damping effect of the floating plate track can be determined according to the support reaction force on the floating plate and the acceleration of the floating plate, and then in the embodiment of the present application, after different parameters are set, the support reaction force on the floating plate and the acceleration of the floating plate can be obtained by performing dynamic simulation calculation through MATLAB simulation software, and then the vibration damping effect of the floating plate track can be determined.

The following will demonstrate the effects of the present application in conjunction with specific embodiments:

several conventional vibration isolators were used in the floating slab track system for analysis, and the key parameters of several conventional vibration isolators were listed in parallel, as shown in table 1. In the embodiment, the operation conditions of 80km/h vehicle speed and American level 5 uneven spectrum with the wavelength of 0.1m-30m are adopted.

TABLE 1

In the present embodiment, the track size of the floating plate may be 25m × 3.2m × 0.3m, and the density may be 2500kg/m³And the rigidity coefficient of the positive rigidity elastic part in the floating slab track is 10 kN/mm. According to the limit of the installation space of the vibration isolator below the floating plate of 450mm multiplied by 450mm (length multiplied by width), 2 negative stiffness spring elastic parts are adopted, the horizontal length L is 200mm, the length L of the negative stiffness elastic part in the free state is 300mm, and sin alpha of the negative stiffness elastic part in the initial installation state is 0.01. The stiffness coefficient of the vibration isolator is selected to be 5kN/mm, and the stiffness coefficient of the elastic part with negative stiffness can be calculated to be 5kN/mm according to the first relational expression. In addition, the damping parameter F of the damping piece can be calculated through the sixth relational expression_dIs 0.8 kN. Simultaneously, each parameter of getting in this application isolator can satisfy and makes the orbital maximum displacement volume of floating slab no longer than 3mm, consequently accords with the safe driving requirement of vehicle.

In the following analysis in combination with the time domain and the frequency domain, in the embodiment of the present application, the vibration isolator of the present application may be named as "ultra-low frequency high damping nonlinear vibration isolator", and in the following description, the vibration isolator provided by the present application is replaced by "ultra-low frequency high damping nonlinear vibration isolator".

Comparing the conventional steel spring and the quasi-zero stiffness vibration isolator respectively, as shown in fig. 8; comparing the conventional steel spring and the magnetorheological damping vibration isolator, as shown in fig. 9; comparing the traditional steel spring with the ultra-low frequency high damping nonlinear vibration isolator, as shown in fig. 10.

In conjunction with fig. 8, 9 and 10, it can be seen from the time domain perspective that: the maximum value of the support reaction force of the traditional steel spring vibration isolator is 26.18 kN; the maximum value of the support reaction force of the magnetorheological damping vibration isolator is 25.00 kN; the maximum value of the support reaction force of the quasi-zero stiffness vibration isolator is 19.78kN, and the maximum value of the support reaction force of the ultralow-frequency high-damping nonlinear vibration isolator is 19.02 kN. Therefore, it can be seen that when the ultra-low frequency high damping vibration isolator is used, the support reaction force under the floating plate is minimum, and is reduced by 27.35% compared with the steel spring floating plate rail.

In the embodiment provided by the present application, the support reaction force of the floating plate can be obtained by adding the support reaction forces received by each vibration isolator below the floating plate, and the support reaction forces of the vibration isolators can be directly compared since the number of vibration isolators below the floating plate is the same when performing the comparison experiment.

From the analysis of the frequency domain, it can be found that: the amplitude of the bearing reaction force of the traditional steel spring vibration isolator is 1.55kN at 10Hz (the fundamental frequency of a floating plate in a floating plate track). After the magneto-rheological damping vibration isolator is adopted, the amplitude of the support reaction force is reduced to 0.57kN and reduced by 63.22 percent near the natural frequency of 10 Hz. After the quasi-zero stiffness vibration isolator is adopted, the natural frequency of the floating plate is reduced to be near 6.3Hz, the amplitude of the support reaction force is 0.61kN, and the reduction is 60.65%.

Furthermore, after the ultralow-frequency high-damping nonlinear vibration isolator is adopted, the branch reaction force amplitude is only 0.32kN at the position where the one-third octave center frequency is 5Hz, and is reduced by 79.35%.

The vibration damping effect of the ultralow-frequency high-damping nonlinear vibration isolator is further analyzed from the acceleration of the floating plate:

analysis was also performed from the time domain angle and the frequency domain angle, comparing the conventional steel spring with the quasi-zero stiffness vibration isolator, as shown in fig. 11, the conventional steel spring with the magnetorheological damping vibration isolator, as shown in fig. 12, and the conventional steel spring with the ultra-low frequency high damping nonlinear vibration isolator, as shown in fig. 13, respectively.

Combining fig. 11, 12 and 13; in connection with the time domain angle it can be seen that: the maximum value of the vertical vibration acceleration of the traditional steel spring floating plate rail is 12.25m/s²(ii) a Maximum value of vertical vibration acceleration of track of floating plate of magneto-rheological damping vibration isolator is 11.37m/s²Only 7.18% reduction; maximum value of vertical vibration acceleration of quasi-zero stiffness vibration isolator floating slab track is 11.15m/s²Only decrease8.98 percent; the maximum value of the vertical vibration acceleration of the floating plate rail of the ultralow-frequency high-damping nonlinear vibration isolator is only 4.88m/s²The reduction was about 60.16%.

From the analysis of the frequency domain, it can be seen that: the vibration level of the vertical vibration acceleration of the traditional steel spring floating plate rail is about 115.55dB around the natural frequency of 10 Hz. Compared with a steel spring floating slab track, the vibration level of the vertical vibration acceleration of the floating slab track adopting the magneto-rheological damping vibration isolator is 106.64dB at 10Hz, and is reduced by 8.91 dB; by adopting the quasi-zero stiffness vibration isolator, the natural frequency of the floating plate is reduced to be near 6.3Hz, and the vibration level of vertical vibration acceleration is 106.41dB, which is reduced by 9.14 dB; by adopting the ultralow-frequency high-damping nonlinear vibration isolator, the natural frequency of the floating plate track is reduced to 6.3Hz, and the vertical vibration acceleration is reduced to 94.95dB, which is about 22.6dB lower than the vertical vibration acceleration at the fundamental frequency of the steel spring floating plate track.

Therefore, compared with the other three common vibration isolators, the ultralow-frequency high-damping vibration isolator effectively inhibits the transmission of the bearing reaction force in the floating slab track on one hand, and on the other hand, the natural frequency of the floating slab track is reduced, so that the low-frequency vibration isolation frequency band range of the bearing reaction force of the floating slab is improved. Vibration can be well suppressed.

Referring to fig. 14, the present application further provides a block diagram of a parameter determining apparatus 10 for a vibration isolator, the vibration isolator including: a positive stiffness elastic member, a negative stiffness elastic member and a controllable damping member; the apparatus 10 comprises:

the first data obtaining module 110 is configured to obtain the stiffness coefficient according to a preset maximum deformation of the vibration isolator in a vertical vibration direction.

A second data obtaining module 120, configured to obtain an initial length of the negative stiffness spring, a number of the negative stiffness springs installed in the vibration isolator, and a length of the negative stiffness spring when the negative stiffness spring is perpendicular to the positive stiffness spring.

A building module 130, configured to build a first relation between the stiffness coefficient of the vibration isolator and the negative stiffness coefficient, the positive stiffness coefficient, the initial length, the number of mounts, and the length; and the value of the stiffness coefficient of the vibration isolator is required to meet the condition that the maximum deformation of the vibration isolator in the vertical vibration direction is smaller than a preset maximum deformation.

And the parameter determining module 140 is configured to calculate the negative stiffness coefficient according to the first relation when the stiffness coefficient of the vibration isolator takes a minimum value within a range of a desired value.

Optionally, the parameter determination module 140 comprises:

a second relation determining module, configured to obtain a second relation between a force applied to the vibration isolator in a vertical vibration direction and a deformation of the vibration isolator in the vertical vibration direction, where in the second relation, the force applied to the vibration isolator in the vertical vibration direction is positively correlated with a positive stiffness coefficient of the positive stiffness elastic member and a damping force of the controllable damping member, and the force applied to the vibration isolator in the vertical vibration direction is also correlated with the initial length, the number of the installed vibration members, the length, and the negative stiffness coefficient;

and the first relational expression determining module is used for obtaining the first relational expression by differentiating the deformation quantity in the second relational expression.

Optionally, the second relation is:

for the speed of shortening of said positive stiffness member, k_vThe positive stiffness coefficient is determined by the preset maximum deformation amount x, L is the length of the negative stiffness elastic member when the negative stiffness elastic member is perpendicular to the positive stiffness elastic member, and L isThe initial length of the negative stiffness elastic parts, n is the number of the negative stiffness elastic parts and is k_hThe negative stiffness coefficient.

Optionally, the second relation determining module includes:

a first establishing module, configured to establish a third relation: f ═ F_v+F_i；

a second establishing module, configured to establish a fourth relation: f ═ F_v+F_hsinα；

a third establishing module, configured to establish a fifth relation:

and the first determining module is used for obtaining the second relational expression according to the third relational expression, the fourth relational expression and the fifth relational expression.

Optionally, after calculating the negative stiffness coefficient according to the first relation, the apparatus further comprises:

and the judging module is used for judging whether the negative stiffness coefficient is larger than the stiffness coefficient of the vibration isolator.

The second determination module is used for reducing the available value range of the stiffness coefficient of the vibration isolator from a minimum value to a preset interval and determining a new available value range of the stiffness coefficient of the vibration isolator when the negative stiffness coefficient is larger than the stiffness coefficient of the vibration isolator;

and the calculation module is used for calculating the negative stiffness coefficient according to the first relational expression when the new minimum value of the stiffness coefficient of the vibration isolator is within the range of the available value.

Optionally, the first relation is:

Optionally, the apparatus further comprises:

the acquisition module is used for acquiring the number of the vibration isolators below the floating plate and the support reaction force borne by the vibration isolators below the floating plate;

and the third determining module is used for determining the damping force parameter of the controllable damping part according to the number of the vibration isolators and the support reaction force on the vibration isolators.

The application also provides an ultra-low frequency high damping isolator, include: a positive stiffness elastic member, a negative stiffness elastic member and a controllable damping member; wherein the negative stiffness coefficient of the negative stiffness elastic member and the damping force of the controllable damping member are determined by the above-mentioned method.

The application also provides a track, including rail, floating plate and foretell ultralow frequency high damping isolator, the rail set up in floating plate top to through the buckling piece with floating plate connects, ultralow frequency high damping isolator set up in floating plate below.

The present application also provides a readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the method as described above.

In the ultralow-frequency high-damping vibration isolator and the parameter determination method, device and track provided by the embodiment of the application, the positive stiffness elastic part, the negative stiffness elastic part and the controllable damping part are combined with each other in the vibration isolator, and the parameters of the positive stiffness elastic part, the negative stiffness elastic part and the controllable damping part are determined by using the method, so that the vibration isolator has good performance effects on reducing the natural frequency and inhibiting vibration. And when the vibration isolator is applied to a track system, the vibration hazard caused by a train running on the track can be well reduced.

In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method may be implemented in other ways. The apparatus embodiments described above are merely illustrative, and for example, the flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods and computer program products according to various embodiments of the present application. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

In addition, functional modules in the embodiments of the present application may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.

The functions, if implemented in the form of software functional modules and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present application or portions thereof that substantially contribute to the prior art may be embodied in the form of a software product stored in a storage medium and including instructions for causing a computer device (which may be a personal computer, a notebook computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes. It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.

The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method of determining parameters of a vibration isolator, the vibration isolator comprising: a positive stiffness elastic member, a negative stiffness elastic member and a controllable damping member;

obtaining a positive stiffness coefficient of the positive stiffness elastic part according to a preset maximum deformation of the vibration isolator in a vertical vibration direction;

deriving the deformation quantity in the second relational expression to obtain a first relational expression;

the value of the stiffness coefficient of the vibration isolator is required to meet the preset maximum deformation quantity of the vibration isolator in the vertical vibration direction, wherein the maximum deformation quantity of the vibration isolator in the vertical vibration direction is smaller than the preset maximum deformation quantity;

2. The method of claim 1, wherein the second relationship is:

for the speed of shortening of said positive stiffness member, k_vThe positive stiffness coefficient is determined by the preset maximum deformation amount x, L is the length of the negative stiffness elastic member when the negative stiffness elastic member is perpendicular to the positive stiffness elastic member, L is the initial length of the negative stiffness elastic member, n is the number of the negative stiffness elastic members, k is the maximum deformation amount x, n is the initial length of the negative stiffness elastic member, n is the number of the negative stiffness elastic members, k is the maximum deformation amount x, and_his the negative stiffness coefficient.

3. The method of claim 2, wherein the second relationship is obtained by:

establishing a third relation: f ═ F_v+F_i；

Wherein, F_vIs the sum of the forces applied to the positive stiffness elastic member and the controllable damping member in the vertical vibration direction, F_iThe component force of the negative stiffness elastic part projected to the shortening direction of the positive stiffness elastic part;

establishing a fourth relation: f ═ F_v+F_h sinα；

Wherein, F_hIs the force applied to the negative stiffness elastic member, and alpha is the remainder of the acute angle between the negative stiffness elastic member and the positive stiffness elastic memberThe angle of the corner is such that,

establishing a fifth relation:

4. The method of claim 2, wherein after calculating the negative stiffness coefficient according to the first relationship, the method further comprises:

5. The method of claim 1, further comprising:

6. A parameter determination device for a vibration isolator, the vibration isolator comprising: a positive stiffness elastic member, a negative stiffness elastic member and a controllable damping member; the device comprises:

the first data acquisition module is used for acquiring a positive stiffness coefficient according to a preset maximum deformation of the vibration isolator in the vertical vibration direction;

a second data acquisition module, configured to acquire an initial length of the negative stiffness elastic member, a number of the negative stiffness elastic member installed in the vibration isolator, and a length of the negative stiffness elastic member when the negative stiffness elastic member is perpendicular to the positive stiffness elastic member;

the construction module is used for acquiring a second relational expression between the force of the vibration isolator in the vertical vibration direction and the deformation of the vibration isolator in the vertical vibration direction, wherein in the second relational expression, the force of the vibration isolator in the vertical vibration direction is positively correlated with the positive stiffness coefficient of the positive stiffness elastic part and the damping force of the controllable damping part, and the force of the vibration isolator in the vertical vibration direction is also correlated with the initial length, the installation number, the length and the negative stiffness coefficient; deriving the deformation quantity in the second relational expression to obtain a first relational expression; the value of the stiffness coefficient of the vibration isolator is required to meet the condition that the maximum deformation of the vibration isolator in the vertical vibration direction is smaller than a preset maximum deformation;

7. An ultra-low frequency high damping vibration isolator, comprising: a positive stiffness spring, a negative stiffness spring and a controllable damper, wherein the negative stiffness coefficient of the negative stiffness spring is determined by the method of any one of claims 1-4.

8. The ultra low frequency high damping vibration isolator of claim 7 wherein the damping force of the controllable damping member is determined by the method of claim 5.

9. A track comprising a steel rail, a floating slab, and the ultra-low frequency high damping vibration isolator of claim 8, wherein the steel rail is disposed above the floating slab and connected to the floating slab by a fastener, and the ultra-low frequency high damping vibration isolator is disposed below the floating slab.