CN112329168B - 3D numerical simulation method for vibration reduction effect of particle damper under two-dimensional vibration condition - Google Patents

3D numerical simulation method for vibration reduction effect of particle damper under two-dimensional vibration condition Download PDF

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CN112329168B
CN112329168B CN202011206006.6A CN202011206006A CN112329168B CN 112329168 B CN112329168 B CN 112329168B CN 202011206006 A CN202011206006 A CN 202011206006A CN 112329168 B CN112329168 B CN 112329168B
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王延荣
刘彬
魏大盛
唐伟
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Abstract

The invention discloses a 3D numerical simulation method for the vibration attenuation effect of a particle damper under a two-dimensional vibration condition, which can realize vibration simulation of 6 scene conditions in a two-dimensional plane by modifying an external excitation module of a numerical model of the particle damper so as to predict the vibration attenuation effect of the particle damper under the corresponding vibration condition. Compared with the existing experiment, the numerical simulation method provided by the invention has higher accuracy.

Description

3D numerical simulation method for vibration reduction effect of particle damper under two-dimensional vibration condition
Technical Field
The invention belongs to a numerical simulation means of a vibration and noise reduction technology, and particularly relates to a 3D numerical simulation method for the vibration reduction effect of a particle damper under a two-dimensional vibration condition, wherein the vibration reduction effect of the particle damper can be predicted to generate vibration in a two-dimensional plane.
Background
The particle damping has wide application prospect under the condition of extreme temperature, is often used for vibration suppression under extreme working conditions in the field of aerospace due to the extremely wide temperature application range, and shows good vibration reduction effect. However, at present, because of a plurality of influencing factors, the design mode is complex, and the damping effect has high nonlinearity, the application is limited. Only the vibration exciting mode and the vibration exciting magnitude of the damper cavity are different, and the vibration damping performance is affected. So far, most researches only can simulate the particle damper under one-dimensional vibration conditions (limited to the horizontal direction or the vertical direction), and the obtained conclusion is difficult to popularize, and even different simulation models can generate seemingly contradictory conclusions. For this reason, the influence of the vibration mode of the damper is not negligible except for the difference in the specifications of the damper itself.
Disclosure of Invention
Aiming at the problems, the invention provides a 3D numerical simulation method for the vibration attenuation effect of the particle damper under the two-dimensional vibration condition, so that the vibration attenuation effect of the given particle damper under different vibration forms can be more comprehensively known, the motion track of the damper is closer to the reality, and the accuracy of numerical simulation is improved.
The invention provides a 3D numerical simulation method for the vibration reduction effect of a particle damper under a two-dimensional vibration condition, which is characterized by comprising the following steps of: the method is realized by the following steps:
step 1: establishing a discrete element model of the particle damper;
(1) establishing a 3D particle damper numerical model capable of describing two-dimensional vibration;
(2) establishing an internal particle model;
step 2: setting external excitation parameters according to the vibration mode characteristics and the application scene;
the external excitation parameters are set as follows:
setting external excitation parameters for 6 scenes, specifically:
scene 1: when the particle damper is free to vibrate only in the horizontal or vertical direction, the external excitation force Fext1And Fext2All set to 0, and simultaneously fix the displacement of the motion dimension without amplitude to 0;
scene 2: when the particle damper is arranged on a slope to perform reciprocating vibration, the included angle between the motion track and the gravity is a fixed value, and no external exciting force exists, the included angle gamma exists between the vibration track and the vertical direction, at the moment, the vibration track is converted into free vibration in the vertical direction to be processed, and the fixed gravity acceleration is changed into g.sin gamma;
scene 3: when the particle damper generates one-dimensional forced vibration in the horizontal or vertical direction, the logarithmic numerical model can set external exciting force according to actual conditions in the vibration direction, and the exciting force and displacement constraint of the particle damper are set to be 0 in the vibration-free dimension;
scene 4: when the particle damper is arranged on a slope to perform reciprocating vibration, the included angle between the motion track and the gravity is a fixed value, and the amplitude of the external excitation force is F along the direction of the included angleextTime, need to be on the excitation force amplitude FextDecomposed to horizontal amplitude Fext1Is Fextsin gamma, vertical amplitude Fext2Is Fext cosγ；
Scene 5: when the particle damper is interfered by exciting forces in two directions perpendicular to each other, the exciting frequency omega in one direction1Natural frequency omega of damper attachment structurenWhen the particle dampers are close to each other, the structures resonate, and the structural response in the direction is much larger than that in the other direction, so that the direction is considered as the main vibration damping direction of the particle dampers, and the external excitation in the other direction is considered as the excitation interference to the particle dampers. At this point, the numerical model can be logarithmic according to phi1＝φ2，ω1＝I1ωn，ω2＝I2ωnIn which I1、I2Multiple of excitation frequency in horizontal and vertical directions, Fext1And Fext2Setting according to actual action conditions.
Scene 6: when the particle damper performs a circular or quasi-circular motion (for example, the particle damper is attached to a fan blade with a rotating shaft in a horizontal direction), an excitation force is generated on the damper in a track tangential direction, and at the moment, the excitation force can be according to omegan＝ω1＝ω2，Fext1＝Fext2，φ1≠φ2The normalized phase difference Δ Φ' is (Φ)2-φ1) The parameter setting of/pi is used for processing the model and can be used for simulating the vibration reduction effect of the damper when the damper generates curve motion track vibration.
And step 3: and (3) carrying out numerical simulation according to the particle damper discrete element model established in the step (1) and the external excitation parameters set in the step (2).
The invention has the advantages that:
1. the numerical prediction of the vibration reduction effect of the particle damper under various curvilinear motion tracks can be realized, and the motion track of the damper is closer to the reality.
2. A plurality of key parameters influencing the damping effect of the particle damper are introduced into an external excitation module, so that the particle damper under more vibration states can be subjected to numerical simulation, and the research range of the damping effect of the particle damper is effectively expanded.
3. The method well inherits the operational advantage of carrying out numerical simulation of the particle motion trajectory by adopting a discrete unit method, and has higher calculation efficiency for simulating the vibration reduction effect of the large-scale particle clusters.
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FIG. 1 is a flow chart of a 3D numerical simulation method of the vibration reduction effect of a particle damper under a two-dimensional vibration condition according to the present invention;
FIG. 2 is a 3D particle damper numerical model that can describe two-dimensional vibrations.
FIG. 3(a) is a schematic diagram of interparticle collisions.
Fig. 3(b) is a schematic diagram of the collision between the particles and the cavity.
Fig. 4 is a schematic diagram of an included angle γ between the vibration trajectory and the vertical direction.
FIG. 5 is a schematic diagram of the arrangement of particle damping within the cavity.
FIG. 6 is a comparison of experimental values with the numerical simulation values of the present invention.
FIG. 7(a), (b), (c), (d), (e), (f) are the effect of particle damping on the cavity response trajectory under two-dimensional excitation conditions of different frequency ratios λ', respectively.
FIGS. 8(a), (b), (c), (d), (e), (f) are graphs of the effect of particle damping on the trajectory of cavity motion when there is a phase difference in the two-dimensional excitation.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention discloses a 3D numerical simulation method of vibration attenuation effect of a particle damper under a two-dimensional vibration condition, which comprises the following specific steps as shown in figure 1:
step one, establishing a discrete element model of the particle damper.
(1) And establishing a 3D particle damper numerical model capable of describing two-dimensional vibration.
The 3D particle damper numerical model, which can describe two-dimensional vibration, includes a particle cavity and a plurality of particles inside the particle cavity. Setting a) all particles to be spherical and the geometric parameters and the physical parameters to be the same; b) the individual computation time steps are small enough that the small perturbations that occur due to a collision at any instant in time are not amplified over time. In the time step, the state information such as displacement, speed and the like of each particle is kept unchanged; c) in the event of a collision, there is a small amount of deformation (normal and tangential overlap) between the particles, but still a small amount compared to the geometric dimensions of the particles.
Let u and w represent the horizontal and vertical displacements of the cavity with respect to the equilibrium position, respectively, and as shown in fig. 2, the equation of motion of the cavity is obtained as:
Figure GDA0002839655900000031
wherein, the expression 'represents a first derivative with time, the expression' represents a second derivative with time, M, K and C respectively represent equivalent mass, equivalent rigidity and equivalent damping of a main structure, and Fcu、FcwIndicating the forces of the particles in the horizontal and vertical directions on the particle cavity. F on the rightmost side of the equationext1、Fext2、ω1、ω2、φ1、φ2The excitation force amplitude, the excitation frequency and the phase in the horizontal and vertical directions are respectively represented. In practical application, the three-dimensional particle cavity shown in fig. 2 is used for representing a main structure for installing the particle damper, the main structure is usually a continuum, the main structure can be simplified by adopting a vibration model with the same two-direction parameters, and the simulation precision is high. The mass, stiffness and damping matrices of the particle cavity in both directions in equation 1 are decoupled, and the vibration model shown in fig. 2 remains a linear system when there are no particles inside the particle cavity. After the particle cavity is filled with particles, due to the existence of oblique collisions between particles and between particles and the cavity, as shown in fig. 3(b), normal and tangential forces between particles and the cavity coexist, thereby coupling the motion of the cavity along two directions.
② the particle cavity in the particle cavity model contains 2 translational freedom degrees, the particleIt contains 6 degrees of freedom (3 directions of translation and 3 directions of rotation). At a certain instant, particle i may collide with several adjacent particles or cavity walls at the same time. For the purpose of analysis, the collision force experienced by particle i is divided into two components (where microscopic forces between particles, such as van der waals forces, etc.), and is not considered): one part is the resultant force and resultant moment caused by the collision between particles, i.e., the internal acting force of the particle, and the other part is the resultant force and resultant moment caused by the collision between particles and the wall surface of the cavity, and the gravity and centrifugal force applied to the particle, which are collectively referred to as the external acting force of the particle. FIG. 3(a), (b) show the particle-to-particle and particle-to-cavity collision models, and Table 1 lists the parameters associated with the collision, where r isi，rj，Pi，Pj，Vi，Vj，ωi，ωjThe particle diameters, displacement vectors, velocity vectors, and angular velocity vectors of the particles i and j are shown, respectively. The displacement vector, velocity vector and wall unit normal vector of the cavity wall b are respectively expressed as Pb，VbAnd nib。
TABLE 1 correlation parameters of particle-to-particle and particle-to-cavity collisions
Figure GDA0002839655900000041
③ the equation of motion of the particle i is as follows:
Figure GDA0002839655900000042
Figure GDA0002839655900000043
wherein m isiDenotes the mass of the particles I, IiIs the moment of inertia of the particle about the center of mass, and g is the acceleration of gravity. ThetaiIs the angular velocity vector of the particle, fnij、fnibRespectively particles and granulesNormal force vector with cavity, ftij、ftibThen the corresponding tangential force vector. n is a radical of an alkyl radicalpair、bpairRespectively, the total number of particles and the total number of cavities that come into contact with the particles i in a certain time calculation step. As can be seen from fig. 3(a), (b), when the particles collide obliquely, the tangential force acting on the contact point generates a moment, which causes the particles to rotate.
If the numerical simulation of the particle motion is to be realized, a contact model capable of accurately describing the particle collision process is required to be provided. The contact model includes two types, a normal contact model and a tangential contact model. The normal contact model adopted by the invention is a TS nonlinear viscoelastic model based on Hertz contact theory. Taking the contact between particle i and particle j as an example, the expression of the normal contact model is as follows:
Figure GDA0002839655900000044
it can be seen that the normal force fnIs a linear elastic force fnsAnd a damping force f reflecting the energy dissipationndIn which the damping force fndIn a particular form proposed by Tsuji et al when studying fluidized beds1. The normal crash damping constant η in the formula can be expressed as a restitution coefficient RnFunction of knpThe equivalent spring rate when two balls contact is represented by the following expression:
Figure GDA0002839655900000051
in the formula, Ei、EjAnd upsiloni、υjThe modulus of elasticity and Poisson's ratio of the colliding particle i and particle j, respectively, and the corresponding equivalent spring rate when a particle collides with the cavity wall surface can be written as
Figure GDA0002839655900000052
Wherein E iscAnd upsiloncRespectively, the modulus of elasticity and the poisson's ratio of the cavity.
The tangential contact model adopted by the invention is a coulomb friction model which is commonly adopted at present, the expression is simple, and the calculation precision is satisfactory. Equation 7 for the friction model is given by taking particle i and particle j as examples, and the expression between the particle and the cavity is the same.
ftij＝-μd|fnij|τij (7)
Wherein mudIs the coefficient of friction from particle to particle and from particle to cavity.
(2) And establishing an internal particle model.
Firstly, setting parameters of particles, including the number n of the particles, the particle diameter r, the normal collision damping constant eta, the elastic modulus E and Poisson ratio upsilon of the particles, and the friction coefficient mu between the particles and the cavitiesd(ii) a Secondly, setting initial positions of the particles, such as: the particle clusters are arranged at the bottom of the cavity along the gravity direction according to a cubic unit cell format, and the translation speed and the rotation speed of each particle are both zero, as shown in fig. 4, the positions of the particle clusters generated by the method are different from the actual positions, but the method has high efficiency and has little influence on numerical simulation.
(3) Establishing a finite element model aiming at a main structure to be provided with a particle damper in CAE pretreatment software, adopting mode analysis of vibration mode normalization, solving by using an energy method to obtain the equivalent mass M and the rigidity K of the main structure, and setting the structural damping C according to actual needs. L, W, H values are set according to the actual length, width and height of the damper cavity, and the elastic modulus E is determined according to the cavity materialcAnd poisson ratio upsiloncAnd further completing the establishment of a 3D particle damper numerical model capable of describing two-dimensional vibration.
Step two: and setting external excitation parameters according to the vibration mode characteristics and the application scene.
In the method, one-dimensional and two-dimensional main vibration types are considered, specifically, the following 6 scenes are considered, and the vibration type track type and the excitation mode are mainly considered when excitation parameters are set for different scenes, specifically, the method comprises the following steps:
scene 1: when the particle damper freely vibrates only in the horizontal or vertical direction, the particle damper can be understood as one-dimensional horizontal or vertical free vibration, and the external excitation force Fext1And Fext2Are all set to 0 while the displacement of the dimension of motion without amplitude is fixed to 0 (displacement constraint is applied).
Scene 2: when the particle damper is arranged on a slope to perform reciprocating vibration, the included angle between the motion track and the gravity is a fixed value, and no external exciting force exists, the motion of the particle damper can be understood as two-dimensional free vibration, the included angle gamma exists between the vibration track and the vertical direction, as shown in fig. 5, because no motion exists in the direction vertical to the plane of the slope, the particle damper can be converted into free vibration processing in the vertical direction, and the fixed gravity acceleration is changed into g · sin gamma.
Scene 3: when the particle damper generates one-dimensional forced vibration in the horizontal or vertical direction, the logarithmic numerical model can set external exciting force according to actual conditions in the vibration direction, and the exciting force and displacement constraint of the particle damper are set to be 0 in the vibration-free dimension.
Scene 4: when the particle damper is arranged on a slope to perform reciprocating vibration, the included angle between the motion track and the gravity is a fixed value, and the amplitude of the external excitation force is F along the direction of the included angleextWhen it is understood that two-dimensional forced vibration is required, the amplitude F of the exciting force is requiredextDecomposed to horizontal amplitude Fext1Is Fextsin gamma, vertical amplitude Fext2Is Fext cosγ。
The external exciting force FextThe method comprises the following steps:
taking the horizontal direction as an example, when the damper is subjected to a fixed displacement a in the horizontal direction01Excitation frequency of omega1At excitation of (D), Fext1＝M a01ω1 2The excitation acceleration is a01ω1 2。
Scene 5: when the particle damper is interfered by exciting forces in two directions perpendicular to each other, the exciting frequency omega in one direction1Natural frequency omega of damper attachment structurenWhen the particle dampers are close to each other, the structures resonate, and the structural response in the direction is much larger than that in the other direction, so that the direction is considered as the main vibration damping direction of the particle dampers, and the external excitation in the other direction is considered as the excitation interference to the particle dampers. At this point, the numerical model can be logarithmic according to phi1＝φ2，ω1＝I1ωn，ω2＝I2ωnIn which I1、I2Multiple of excitation frequency in horizontal and vertical directions, Fext1And Fext2Setting according to actual action conditions.
Scene 6: when the particle damper performs a circular or quasi-circular motion (for example, the particle damper is attached to a fan blade with a rotating shaft in a horizontal direction), an exciting force is generated to the damper along a tangential direction of a track, and then the exciting force can be according to omegan＝ω1＝ω2，Fext1＝Fext2，φ1≠φ2The normalized phase difference Δ Φ' is (Φ)2-φ1) The parameter setting of/pi is used for processing the model and can be used for simulating the vibration reduction effect of the damper when the damper generates curve motion track vibration.
Step three: and (3) carrying out numerical simulation according to the particle damper discrete element model established in the step (1) and the external excitation parameters set in the step (2).
Firstly, basic parameters of a model are set, and the basic parameters mainly comprise three parts: (1) particle cavity parameters: m, K and C respectively represent the mass, equivalent rigidity and equivalent damping of the equivalent particle cavity, L, W, H respectively represent the length, width and height of the cavity, and the elastic modulus E of the cavitycAnd poisson ratio upsilonc(ii) a (2) Particle parameters: comprises the particle number n, the particle diameter r, the normal collision damping constant eta, the particle elastic modulus E and the Poisson ratio upsilon, and the friction coefficient mu between particles and between cavitiesd(ii) a (3) Excitation parameters: amplitude F of the excitation force in the horizontal and vertical directionsext1、Fext2Excitation frequency omega1、ω2Phase phi1、φ2。
Subsequently, the operation is started to determine the position of the cavity and the particles inside the cavity. For particle i, if presentIn contact pairs and normal to the pairsn>0, calculating corresponding normal and tangential contact forces by using the formulas 4 and 7; if the normal direction overlapping amount deltanAnd (5) setting all the contact forces to be 0 when the contact force is less than or equal to 0.
Then, summing the vectors of all the forces (including internal and external forces) acting on the particle i; then, the translational acceleration and the rotational acceleration of the particle i are solved by using the formula 2 and the formula 3, and the motion equation of each of the rest particles is solved according to the process.
Finally, the resultant force acting on the cluster of particles is solved. According to Newton's third law, the acting force of the particles on the cavity is obtained, and the acting force is decomposed along the horizontal and vertical directions to obtain FcuAnd FcwThen, the motion state of the cavity is updated by using the formula 1, and the next cycle is entered.
The invention provides a method for realizing 3D numerical simulation of a particle damper generating two-dimensional vibration by modifying an external excitation module of a particle damper numerical model. The method can realize the vibration of 6 vibration scenes in a two-dimensional plane and has higher accuracy.
Example (b):
the parameters of a main structure needing vibration reduction are as follows: the main structure mass M is 0.293kg, the equivalent damping coefficient C is 0.116, and the equivalent stiffness K is 1602.7N/M. The natural modal frequency of the main structure is fn11.771Hz, the inherent damping ratio zeta of the structure is 0.268%.
According to engineering requirements, a particle damper is designed. 200 Acrylic resin (Acrylic resin) particles with diameter d of 6mm are filled in the particle cavity, and the mass ratio m of the Acrylic resin particlesr9.2%. The density of the particles is 1190kg/m3The coulomb friction coefficient μ is 0.52, and the contact damping constant η is 0.077. Modulus of elasticity E of the particlesp331.37MPa, modulus of elasticity E of the cavityc281.85MPa, Poisson's ratio of granular material is 0.38, and normal contact rigidity between granules is knpp＝107N/m3/2And the normal contact stiffness k between the particles and the cavity wallnpw＝1.3×107N/m3/2。
In one dimension of waterThe comparison with the test values is carried out under flat forced vibration conditions. FIG. 6 shows a horizontal displacement excitation magnitude of a01The comparison of the calculated result and the test value when the diameter is 0.5mm shows that the numerical simulation method has higher accuracy.
(1) Simulation of scenario 5:
the particle damper has the main function of damping vibration in the horizontal direction, so that the excitation frequency omega 1 in the horizontal direction is set to be equal to the system resonance frequency omega in the scenenAnd the vertical direction excitation frequency omega2Is 0.1, 0.5, 1, 2, 5 and 10 times omega respectivelyn。
The basic displacement excitation applied in the horizontal and vertical directions of the present part of the calculation example is 1mm, the phase difference is 0, and corresponding calculation results are given in fig. 7(a), (b), (c), (d), (e) and (f). In fig. 7, the abscissa is the magnification factor in the horizontal direction, and the ordinate is the magnification factor in the vertical direction. It can be seen that under the excitation conditions of different frequencies in the vertical direction, the particle damping can play a stable vibration damping effect in the X direction. When the response amplification factor of fig. 7 is observed, the response amplitude of the cavity filled with particles is reduced by more than 75% compared with the control group, and the influence of external excitation in other directions on the damping of the particles in the principal vibration direction is small.
(2) Simulation of scenario 6:
the damper model used in this scenario is the same as scenario 5, except that the external excitation changes, assuming that the amplitude of the damper in both horizontal and vertical directions is 1mm (a)01＝a021mm) and the excitation frequency is the structural resonance frequency (omega)1＝ω2＝ωn) Is excited by the fundamental displacement. Let Δ φ' become (φ)2-φ1) And/pi, examining the vibration damping effect difference of particle damping when the phase difference delta phi' is respectively 0, 1/6, 1/3, 1/2, 2/3, 5/6 and 1.
Fig. 8(a), (b), (c), (d), (e), (f) show the corresponding calculation results (Δ Φ 'is 0, the trajectory diagram is shown in fig. 7 (c)), and it can be seen that within a given range of Δ Φ', the particle damping can exert good damping effect in both horizontal and vertical directions. In fig. 8, the abscissa is the magnification factor in the horizontal direction, and the ordinate is the magnification factor in the vertical direction. As can be seen from the extreme values of the amplification factors in two directions in FIG. 7, the existence of particle damping causes small difference of the response attenuation amplitudes of the cavities in the horizontal and vertical directions, and the X-direction response amplitude of the cavity provided with the damper is reduced by about 75% and the Y-direction response amplitude of the cavity provided with the damper is reduced by about 70% compared with that of the control group in numerical view.

Claims (4)

1. A3D numerical simulation method for the vibration attenuation effect of a particle damper under a two-dimensional vibration condition is characterized by comprising the following steps of: the method is realized by the following steps:
step 1: establishing a discrete element model of the particle damper;
step 2: setting external excitation parameters according to the vibration mode characteristics and the application scene;
the external excitation parameters are set as follows:
setting external excitation parameters for 6 scenes, specifically:
scene 1: when the particle damper is free to vibrate only in the horizontal or vertical direction, the external excitation force Fext1And Fext2All set to 0, and simultaneously fix the displacement of the motion dimension without amplitude to 0;
scene 2: when the particle damper is arranged on a slope to perform reciprocating vibration, the included angle between the motion track and the gravity is a fixed value, and no external exciting force exists, the included angle gamma exists between the vibration track and the vertical direction, at the moment, the vibration track is converted into free vibration in the vertical direction to be processed, and the fixed gravity acceleration is changed into g.sin gamma;
scene 3: when the particle damper generates one-dimensional forced vibration in the horizontal or vertical direction, the logarithmic numerical model can set external exciting force according to actual conditions in the vibration direction, and the exciting force and displacement constraint of the particle damper are both set to be 0 in the non-vibration dimension;
scene 4: when the particle damper is arranged on a slope to perform reciprocating vibration, the included angle between the motion track and the gravity is a fixed value, and the amplitude of the external excitation force is F along the direction of the included angleextTime, need to be aligned with the exciting force amplitude FextDecomposed to horizontal amplitude Fext1Is Fextsin gamma, vertical amplitude Fext2Is Fext cosγ；
Scene 5: when the particle damper is interfered by exciting forces in two directions perpendicular to each other, the exciting frequency omega in one direction1Natural frequency omega of damper attachment structurenWhen the particle dampers are close to each other, the structures resonate, and the structural response in the direction is much larger than that in the other direction, so that the direction is considered as the main vibration damping direction of the particle dampers, and the external excitation in the other direction is considered as the excitation interference to the particle dampers. At this point, the numerical model can be logarithmic according to phi1＝φ2，ω1＝I1ωn，ω2＝I2ωnIn which I1、I2Multiple of excitation frequency in horizontal and vertical directions, Fext1And Fext2Setting according to the actual action condition;
scene 6: when the particle damper does circular or quasi-circular motion, exciting force can be generated on the damper along the tangential direction of the track, and at the moment, the exciting force can be according to omegan＝ω1＝ω2，Fext1＝Fext2，φ1≠φ2The normalized phase difference Δ Φ' is (Φ)2-φ1) The parameter setting of/pi is used for processing the model and simulating the vibration reduction effect when the damper generates curve motion track vibration;
and step 3: and (3) carrying out numerical simulation according to the particle damper discrete element model established in the step (1) and the external excitation parameters set in the step (2).
2. The 3D numerical simulation method of the vibration attenuation effect of the particle damper under the two-dimensional vibration condition as claimed in claim 1, wherein: in the step 1, the method for establishing the numerical model of the 3D particle damper capable of describing two-dimensional vibration comprises the following steps:
setting a) all particles to be spherical, and the geometric parameters and the physical parameters to be the same; b) the tiny disturbance caused by collision at any moment can not be amplified along with the time advance; in the time step, the state information of the displacement and the speed of each particle is kept unchanged; c) when collision occurs, small deformation quantity can be generated among particles;
firstly, establishing a cavity motion equation;
let u and w represent the horizontal and vertical displacement of the cavity relative to the equilibrium position, respectively, and the equation of motion for the cavity is obtained as:
Figure FDA0003535437080000021
wherein, the expression 'represents a first derivative with time, the expression' represents a second derivative with time, M, K and C respectively represent equivalent mass, equivalent rigidity and equivalent damping of a main structure, and Fcu、FcwRepresenting the forces of the particles on the particle cavity in the horizontal and vertical directions; f on the rightmost side of the equationext1、Fext2、ω1、ω2、φ1、φ2Respectively representing the amplitude, the excitation frequency and the phase of the excitation force in the horizontal direction and the vertical direction;
establishing a particle collision model;
the collision force experienced by particle i is divided into two parts: one part is the resultant force and resultant moment caused by the collision between the particles, namely the internal acting force of the particles, and the other part is the resultant force and resultant moment formed by the collision between the particles and the wall surface of the cavity, and the gravity and centrifugal force borne by the particles, which are collectively called as the external acting force of the particles; then establishing collision models between particles and cavities;
establishing a particle motion equation;
the equation of motion for particle i is as follows:
Figure FDA0003535437080000022
Figure FDA0003535437080000023
wherein m isiDenotes the mass of the particles I, IiIs the moment of inertia of the particle about the center of mass, g is the acceleration of gravity, θiIs the angular velocity vector of the particle, fnij、fnibNormal force vectors between particles and cavities, ftij、ftibThen the corresponding tangential force vector, npair、bpairRespectively representing the total number of particles and the total number of cavities which are in contact with the particles i in a certain time calculation step;
establishing a contact model in the particle collision process;
the contact model comprises a normal contact model and a tangential contact model; the normal contact model between particle i and particle j is:
Figure FDA0003535437080000024
in formula 4, normal force fnIs a linear elastic force fnsAnd a damping force f reflecting the energy dissipationndA resultant force of (a); the normal collision damping constant eta is expressed as a recovery coefficient RnFunction of (a), knpThe equivalent spring rate when two balls contact is represented by the following expression:
Figure FDA0003535437080000025
in the formula, Ei、EjAnd upsiloni、υjThe modulus of elasticity and Poisson's ratio of the colliding particle i and particle j, respectively, and the corresponding equivalent spring rate when a particle collides with the wall surface of the cavity is written as
Figure FDA0003535437080000031
Wherein E iscAnd upsiloncRespectively representing the elastic modulus and the poisson ratio of the cavity;
the tangential contact model between the particle i and the particle j adopts a coulomb friction model formula 7, and the expression between the particle and the cavity is the same as that of the particle;
ftij＝-μd|fnij|τij (7)
wherein mudIs the coefficient of friction from particle to particle and from particle to cavity;
(2) establishing an internal particle model;
firstly, setting parameters of particles, including the number n of the particles, the particle diameter r, the normal collision damping constant eta, the elastic modulus E and Poisson ratio upsilon of the particles, and the friction coefficient mu between the particles and the cavitiesd(ii) a Secondly, setting initial positions of the particles, such as: arranging the particle groups at the bottom of the cavity along the gravity direction according to a cubic unit cell format, and enabling the translation speed and the rotation speed of each particle to be zero;
(3) establishing a finite element model aiming at a main structure for establishing a particle damper to be installed in CAE pretreatment software, adopting mode analysis of vibration mode normalization, solving by using an energy method to obtain equivalent mass M and rigidity K of the main structure, setting structural damping C according to actual requirements, setting L, W, H values according to actual length, width and height dimensions of a damper cavity, and determining elastic modulus E according to cavity materialscAnd poisson ratio upsiloncAnd then completing the establishment of a 3D particle damper numerical model capable of describing two-dimensional vibration.
3. The 3D numerical simulation method of the vibration attenuation effect of the particle damper under the two-dimensional vibration condition as claimed in claim 1, wherein: in scene 4, external excitation force FextThe method comprises the following steps:
taking the horizontal direction as an example, when the damper is subjected to a fixed displacement a in the horizontal direction01Excitation frequency of omega1At excitation of (D), Fext1＝Ma01ω1 2The excitation acceleration is a01ω1 2。
4. The 3D numerical simulation method of the vibration attenuation effect of the particle damper under the two-dimensional vibration condition as claimed in claim 1, wherein: the specific simulation method of the step 3 comprises the following steps:
firstly, basic parameters of a model are set, and the basic parameters mainly comprise three parts: (1) particle cavity parameters: m, K and C respectively represent the mass, equivalent rigidity and equivalent damping of the equivalent particle cavity, L, W, H respectively represent the length, width and height of the cavity, and the elastic modulus E of the cavitycAnd poisson ratio upsilonc(ii) a (2) Particle parameters: comprises the particle number n, the particle diameter r, the normal collision damping constant eta, the particle elastic modulus E and the Poisson ratio upsilon, and the friction coefficient mu between particles and between cavitiesd(ii) a (3) Excitation parameters: amplitude F of the excitation force in the horizontal and vertical directionsext1、Fext2Excitation frequency omega1、ω2Phase phi1、φ2；
Subsequently, the position of the cavity and the particles inside the cavity is determined; for particle i, if there is a contact pair and its normal overlap deltan>0, calculating corresponding normal and tangential contact forces by using the contact model in the particle collision process and the contact model in the particle collision process; if the normal direction overlap amount deltanIf the contact force is less than or equal to 0, all the contact forces are set to be 0;
then, the vector sum is calculated for all the actions acting on the particle i; then, solving the translational acceleration and the rotational acceleration of the particle i by using a particle motion equation, and solving the motion equation of each of the rest particles according to the process;
finally, the resultant force acting on the cluster of particles is solved.
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