CN105369930B - Realize viscous damper position determines in high-level structure processing method and system - Google Patents
Realize viscous damper position determines in high-level structure processing method and system Download PDFInfo
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Abstract
The realization viscous damper of the invention processing method that position determines in high-level structure, comprising: establish standard three-dimensional solid model, including spring K1, spring K2With spring K3*, spring K2With spring K3* connect after with spring K1Parallel connection simultaneously supports particle jointly；Spring K3* equivalent transformation is viscous damper, then standard three-dimensional solid model converts to obtain simulation band viscous damper structural model；Based on simulation band viscous damper structural model, additional damping ratio algorithm is obtained；Derivation and minimizing are carried out to the reciprocal of additional damping ratio algorithm, obtain maximum additional damping ratio algorithm；Maximum damping ratio is calculated by maximum additional damping ratio algorithm；Default damping target value；Additional maximum damping ratio obtains the position of viscous damper setting compared with damping target value.Based on this, additionally provides and realize the viscous damper processing system that position determines in high-level structure.Using the enough positions for fast and accurately determining viscous damper of the technical program.
Description
Technical field
The present invention relates to field of structural design, in particular to a kind of realization viscous damper position in high-level structure determines
Processing method and system.
Background technique
The design of the structures such as structure, bridge structure is built in field of structural design, including mechanism of China Democratic National Construction Association, work.When above-mentioned engineering knot
Structure design is applied at earthquake zone, especially the earthquake zone of highly seismic region when, high-rise or super high rise structure design is mainly by ground
Shake control, traditional design then design method based on " anti-", not only material utilization amount is big, cost is high, but also member section ruler
It is very little " stupid big black thick ", influence the use of building.Therefore, damper, such as viscous (bullet) property can all be applied in such building structure
Damper, fluid damper, the energy consumption in earthquake can be fallen by applying damper, not only saved material, reduced cost, and
And structure size is smaller, can increase the effective usable floor area of building.
However, the 12.3.4 articles of " seismic design provision in building code " GB50011-2010 and its provision illustrate at present, give
Viscous damper is added to the damping ratio approximate estimation formula of structure:
ζ cj=Tj/ (4 π Mj) * φ jTCc φ j=1/2/Kj × ω j φ jTCc φ j
In formula: ζ cj --- the additional damping ratio of viscous damper in the structure jth vibration shape；
Tj --- the period of the structure jth vibration shape；
ω j --- the circular frequency of the structure jth vibration shape；
The structure additional damping matrix that Cc --- efficiency device generates；
Mj --- jth vibration shape generalized mass；
Kj --- jth vibration shape generalized stifflness；
φ j --- the mode factor of the jth vibration shape.
The above-mentioned viscous damper provided is only used for estimation damping value, and the error of the algorithm is larger.
In addition, being that can not implement to viscous damper in which position of structural body and meet work only with the algorithm above
The requirement of journey construction be it is uncertain, increase the difficulty calculated during engineering-built.
Summary of the invention
It is an object of the invention to overcome the problems, such as viscous damper in structural body enforcing location accuracy.
In order to solve the above technical problems, the present invention adopts the following technical scheme:
It is a kind of to realize the viscous damper processing method that position determines in high-level structure, comprising:
Standard three-dimensional solid model is established, the standard three-dimensional solid model includes spring K1, spring K2With spring K3*, institute
State spring K2With the spring K3* connect after with the spring K1Parallel connection simultaneously supports particle jointly；
The spring K3* equivalent transformation is viscous damper, then the standard three-dimensional solid model, which converts, is simulated
Band viscous damper structural model；
Based on the simulation band viscous damper structural model, operation is carried out on complex number space, obtains additional damping ratio
Algorithm；
Derivation and minimizing are carried out to the reciprocal of the additional damping ratio algorithm, obtain maximum additional damping ratio algorithm；
Maximum damping ratio is calculated by the maximum additional damping ratio algorithm；
Default damping target value；
The additional maximum damping ratio obtains the position of viscous damper setting compared with the damping target value.
In one embodiment, the additional maximum damping ratio obtains viscous damping compared with the damping target value
The step of position of device setting specifically:
Obtain the fundamental natural period of vibration T of the standard three-dimensional solid model1；
The position for being used to install viscous damper is connected using rigid rod, then calculates the simulation again with viscous
The fundamental natural period of vibration T of damper structure model2；
According to a=T1/T2With the maximum dampingratioζ max=(a2-1)/4/a calculates position setting viscous damper
It can give structure additional maximum damping ratio；
The additional maximum damping ratio judges that the additional maximum damping ratio is compared with the damping target value
It is no to reach the default damping target value, it is the position for obtaining viscous damper setting.
In one embodiment, the additional maximum damping ratio obtains viscous damping compared with the damping target value
The step of position of device setting further include:
It determines the additional maximum damping ratio and is not up to the default damping target value, then convert viscous damper
Position, and return execute it is described the position for being used to install viscous damper is connected using rigid rod, then calculate institute
State the step of simulating the fundamental natural period of vibration T2 with viscous damper structural model.
In one embodiment, the additional damping ratio algorithm are as follows: ζ=K2 2K3/2/[K1K2 2+K3 2(K1+K2)]；The maximum
Additional damping ratio algorithm are as follows: ζ max=Ki/2Ke；
Wherein, K3=C ω, C are damped coefficient, and ω is frequency, and Ki is the Complex modes of the standard three-dimensional solid model
Imaginary part, Ke are the Complex modes of the standard three-dimensional solid model.
In one embodiment, the mode that the viscous damper is connect with structure includes: diagonal strut, herringbone support, elbow
Formula support or scissors support in any one or more.
In addition, also providing a kind of processing system for realizing viscous damper position determination in high-level structure, comprising:
Standard three-dimensional solid model module, including spring K1, spring K2With spring K3*, the spring K2With the spring K3*
After series connection with the spring K1Parallel connection simultaneously supports particle jointly；
Simulation band viscous damper structural model module, the spring K3* equivalent transformation is viscous damper；
Additional damping ratio computing module, based on the simulation band viscous damper structural model module, on complex number space
It carries out operation and obtains additional damping ratio algorithm；
Maximum additional damping ratio computing module, to the inverse of the additional damping ratio algorithm of the additional damping ratio computing module
Derivation and minimizing are carried out, maximum additional damping ratio algorithm is obtained；
Maximum damping ratio is calculated by the maximum additional damping ratio algorithm in computing module；
Presetting module presets damping target value；
Viscous damper position computing module, the additional maximum damping ratio obtain compared with the damping target value
The position of viscous damper setting.
In one embodiment, viscous damper position computing module includes:
Natural vibration period, arithmetic element, obtained the fundamental natural period of vibration T of standard three-dimensional solid model1；
Arithmetic element natural vibration period is simulated, the position for being used to install viscous damper is connected using rigid rod, so
Fundamental natural period of vibration T of the calculating simulation with viscous damper structural model again afterwards2；
Computing unit, according to a=T1/T2With the maximum dampingratioζ max=(a2- 1)/4/a calculates position setting
Viscous damper can give structure additional maximum damping ratio；
Comparing unit, the additional maximum damping ratio compared with the damping target value, judge it is described it is additional most
Whether big damping ratio reaches the default damping target value, is the position for obtaining viscous damper setting.
In one embodiment, the comparing unit is also used to: it is not up to described to determine the additional maximum damping ratio
Default damping target value, then convert the position of viscous damper, and returns to execution simulation arithmetic element natural vibration period.
In one embodiment, the additional damping ratio algorithm are as follows: ζ=K2 2K3/2/[K1K2 2+K3 2(K1+K2)]；The maximum
Additional damping ratio algorithm are as follows: ζ max=Ki/2Ke；
Wherein, K3=C ω, C are damped coefficient, and ω is frequency, and Ki is the Complex modes of the standard three-dimensional solid model
Imaginary part, Ke are the Complex modes of the standard three-dimensional solid model.
In one embodiment, the mode that the viscous damper is connect with structure includes: diagonal strut, herringbone support, elbow
Formula support or scissors support in any one or more.
As shown from the above technical solution, the advantages and positive effects of the present invention are:
Using the realization viscous damper of this programme processing method and system that position determines in high-level structure, pass through this
The maximum damping ratio of processing method carries out purposive adjustment position compared with preset damping target value.It thus can be with
Quickly, the convenient and accurate determining position range for applying viscous damper, once identified position meets damping target value,
Then determine the position of viscous damper, without really applying viscous damper tentative calculation in high building structure, significantly
Reduce the difficulty calculated during engineering-built.
Detailed description of the invention
Fig. 1 is the schematic diagram of single-degree-of-freedom simplified model；
Fig. 2 is the schematic diagram of the standard three-dimensional solid model in an embodiment；
Fig. 3 is schematic diagram of the simulation with viscous damper structural model in an embodiment；
Fig. 4 is the flow chart that the viscous damper processing method that position determines in high-level structure is realized in an embodiment；
Fig. 5 is the specific flow chart of step S70 in Fig. 4；
Fig. 6 is the diagonal strut form of viscous damper；
Fig. 7 is the herringbone supporting form of viscous damper；
Fig. 8 is the scissors supporting form of viscous damper；
Fig. 9 is the elbow formula supporting form of viscous damper；
Figure 10 is another elbow formula supporting form of viscous damper；
Figure 11 is A illustraton of model；
Figure 12 is A illustraton of model of another angle；
Figure 13 is A inner cylinder support elevation；
Figure 14 is that A top area applies the enlarged diagram of viscous damper；
Figure 15 is that A bottom section applies the enlarged diagram of viscous damper；
Figure 16 is the facade display figure of A application viscous damper；
Figure 17 is the waveform diagram for applying natural wave L0142 principal direction；
Figure 18 is the waveform diagram for applying natural L0142 direction of wave；
Figure 19 is to apply natural wave L0142 fitting spectrum TongAn and comment and standardize to compose to compare figure；
Figure 20 is X to floor maximum relative storey displacement angular curve comparison diagram；
Figure 21 is Y-direction floor maximum relative storey displacement angular curve comparison diagram；
Figure 22 is X to floor maximum shear curve comparison figure；
Figure 23 is Y-direction floor maximum shear curve comparison figure；
Figure 24 is X to floor maximum tilting moment curve comparison figure；
Figure 25 is Y-direction floor maximum tilting moment curve comparison figure；
Figure 26 is the logic diagram for applying the simulation system of viscous damper high-level structure in an embodiment；
Figure 27 is the specific logic diagram of viscous damper position computing module in Figure 26.
Specific embodiment
The exemplary embodiment for embodying feature of present invention and advantage will describe in detail in the following description.It should be understood that
The present invention can have various variations in different embodiments, neither depart from the scope of the present invention, and theory therein
Bright and diagram inherently is illustrated as being used, rather than to limit the present invention.
Fig. 1 is traditional single-degree-of-freedom simplified model, i.e., does not consider that the additional deformation generated because damper is contributed influences.
Fig. 2 is standard three-dimensional solid model, if by spring K3* it is substituted using viscous damper, since viscous damper is contributed to bullet
Spring K2Deformation have an impact, and can be taken into account in the structure of entire standard three-dimensional solid model, so as to effectively consider because
Viscous damper is contributed and the additional deformation that generates in coupled component.
Therefore, in one embodiment, in conjunction with attached drawing 3, the viscous damper place that position determines in high-level structure is realized
Reason method, includes the following steps:
Step S10, establishes standard three-dimensional solid model, and standard three-dimensional solid model includes: spring K1, spring K2And spring
K3*, spring K2With spring K3* connect after with spring K1Parallel connection simultaneously supports particle M jointly.
Step S20, spring K3* equivalent transformation is viscous damper, then standard three-dimensional solid model, which converts, is simulated
Band viscous damper structural model.
Step S30 carries out operation based on simulation band viscous damper structural model on complex number space, obtains additional resistance
Buddhist nun compares algorithm.
Specifically, in conjunction with attached drawing 1~3, on complex number space, it is based on mechanical balance principle and principle of deformation consistency, and draw
Enter Complex modes and energy loss factor concept, the definition based on damping ratio obtains the computational algorithm of additional damping ratio.
The system of the standard three-dimensional solid model is reciprocating under the Simple Harmonic Load P effect that frequency is ω, generation
Simple harmonic quantity is deformed into X, wherein in spring K2With substitution spring K3* the simple harmonic quantity deformation generated in viscous damper is respectively Z1And Z2。
On complex number space, the Complex modes K of viscous damper3*=iK3, wherein K3=C ω, i are the symbol of imaginary number, and C is
Damped coefficient.
According to denaturation coordination principle and the equilibrium principle of power, there is following two equation:
Equation (1): X=Z1+Z2
Equation (2): K3*Z1=K2Z2
X and Z are derived in this way2Respectively equal to:
Equation (3): Z2=K3*/K2×Z1
Equation (4): X=Z1×(1+K3*/K2)
The kinetic balance equation that the standard three-dimensional solid model is established on complex number space is as follows:
Equation (5): P=MX "+K1X+K3*Z1
And then it derives:
Equation (6): P=[- ω2M+K1+K2K3*/(K2+K3*)]×X
It derives:
Equation (7): P/X=K1-ω2M+K2K3*/(K2+K3*)
So Complex modes (or equivalent stiffness) of the standard three-dimensional solid model structure are as follows:
Equation (8): Ke=K1+K2K3*/(K2+K3*)
The K known to aforementioned3*=iK3, so:
K2K3*/(K2+K3*)=iK2K3/(K2+iK3)
=K2K3 2/(K2 2+K3 2)+iK2 2K3/(K2 2+K3 2)
The Complex modes (or equivalent stiffness) of the standard three-dimensional solid model structure in this way are as follows:
Equation (9): Ke=K1+K2K3 2/(K2 2+K3 2)+iK2 2K3/(K2 2+K3 2)
So the real part of the Complex modes (or equivalent stiffness) are as follows:
Equation (10): Kr=K1+K2K3 2/(K2 2+K3 2)
So the imaginary part of the Complex modes (or equivalent stiffness) are as follows:
Equation (11): Ki=K2 2K3/(K2 2+K3 2)
According to Structural Dynamics principle, the additional damping ratio (i.e. additional damping ratio algorithm) of the system are as follows:
Equation (12): ζ=Ki/2Ke
=K2 2K3/2/[K1K2 2+K3 2(K1+K2)]
Step S40 carries out derivation and minimizing to the reciprocal of additional damping ratio algorithm, obtains maximum additional damping ratio and calculate
Method.Specifically:
The inverse of additional damping ratio algorithm (i.e. equation 12) are as follows:
Equation (13): 1/ ζ=K1/K3+(K1+K2)/K2 2×K3
It is the maximum of ζ that the minimum of 1/ ζ is corresponding, therefore peer-to-peer (13) both sides are to K3Derivation, to acquire 1/ ζ's
Minimum obtains following formula:
Equation (14): d (1/ ζ)/d (K3)=- K1/K3 2+(K1+K2)/K2 2
It is equation (14) is zero that the condition of minimum, which occurs, in 1/ ζ, therefore enables equation (14) to be equal to zero and obtain:
Equation (15): K3 2=K1K2 2/(K1+K2)
By front K3*=iK3It is found that ︳ K3* ︳=K3, therefore:
Equation (16): ︳ K3* ︳=K3=K2×SQRT(K1/(K1+K2))
Enable a=SQRT ((K1+K2)/K1), then K3=K2/ a is rewinded into equation (12), then obtains additional maximum dampingratioζ
Max are as follows:
Equation (17): ζ max=Ki/2Ke
=K2 2K3/2/[K1K2 2+K3 2(K1+K2)]
=K2/a/2/[K1+(K1+K2)/a2]
=(a2-1)/4/a
Step S50 obtains maximum damping ratio by maximum additional damping ratio algorithm.
As can be seen that the maximum damping ratio that viscous damper is applied to system is same viscous damper resistance from equation (17)
Buddhist nun's coefficient is no any relationship, and corresponds to damped coefficient when additional damping ratio reaches maximum (i.e. by C ω=K3=K2/
A derives C=K2/ a/ ω), it utilizes in the 12.3.4 articles of " seismic design provision in building code " GB50011-2010 and its provision explanation
The damping ratio that the formula provided is found out is ζ=(a2- 1)/2/a, 2 times of exactly practical additional damping ratio, it is seen that error is big,
And work as C > K2After/a/ ω, with the increase of C value, error increases in divergence expression.
It can be seen that obtaining maximum damping ratio using above-mentioned additional damping ratio algorithm, error can be significantly reduced, work is met
The requirement of Cheng Jingdu.
Further, a=SQRT ((K is inquired into1+K2)/K1) physical meaning: assuming that by spring K shown in Fig. 33* place is disconnected
It opens, then the natural vibration period of the model system is then T1=2 π × SQRT (M/K1)；And by Fig. 3 system in spring K3* place is not with generating
After the rigid rod connection of deformation, then the natural vibration period of the system is T2=2 π × SQRT (M/ (K1+K2)), it is clear that a=SQRT
((K1+K2)/K1)=T1/T2。
Step S60 presets damping target value.Specifically, which can tie according to building structure and building
Earthquake intensity region setting where structure.In addition, presetting the damping target value can set at the very start, can also obtain
Set after maximum damping ratio, can before or after step S10 to step S50 any one step setting.
Step S70 adds maximum damping ratio compared with damping target value, obtains the position of viscous damper setting.
Further, refering to attached drawing 5, step S70 is specifically:
Step S71: the fundamental natural period of vibration T of standard three-dimensional solid model is obtained1。
Step S72: the position for being used to install viscous damper is connected using rigid rod, then calculating simulation band again
The fundamental natural period of vibration T of viscous damper structural model2。
Step S73: according to a=T1/T2With maximum dampingratioζ max=(a2- 1)/4/a calculates the position and viscous resistance is arranged
Buddhist nun's device can give structure additional maximum damping ratio.
Step S74: additional maximum damping ratio judges whether additional maximum damping ratio reaches compared with damping target value
It is the position for obtaining viscous damper setting to default damping target value.
It can be seen that can quick, the convenient and accurate determining position for applying viscous damper using the program.
In other embodiments, step S70 further include:
Step S75: the not up to default damping target value of additional maximum damping ratio is determined, then converts viscous damper
Position, and return to execution and connect the position for being used to install viscous damper using rigid rod, then in calculating simulation band
The fundamental natural period of vibration T of viscous damper structural model2The step of.It in a further embodiment, can also be with return step S71；
In a preferred embodiment, return step S72.
In addition, the movement of above-mentioned viscous damper position can be based on following principle: viscous damper position is in structure
Symmetrically it is arranged.The viscous damper being symmetrically arranged can preferably play the function of viscous damper, and help
The target set point of damping is more easily reachd in structure.
In conclusion being led to using the realization viscous damper of this programme processing method that position determines in high-level structure
The maximum damping ratio for the treatment of method is crossed compared with preset damping target value, carries out purposive adjustment position.Thus
Can quick, the convenient and accurate determining position range for applying viscous damper, once identified position meets damping mesh
Scale value, it is determined that the position of viscous damper, without really applying viscous damper tentative calculation in high building structure,
The difficulty calculated during engineering-built greatly reduces.
In other embodiments, refering to attached drawing 6-10, viscous damper usually requires mechanically to connect with structure
It connects, and in order to allow viscous damper that can play very big effect when the deformation of very little occurs for structure.Therefore this programme is true
Determined the position of viscous damper placement, then it can be by the way of being connect as follows with structure, including diagonal strut, herringbone branch
Support, elbow formula support or scissors support in any one or more.
It can better illustrate this programme using above-mentioned scheme now in conjunction with a specific structure model and realize viscous damping
The accuracy and convenience of the device processing method that position determines in high-level structure.
Setting structure model, referred to as A in the present embodiment, A all uses steel frame-support inner tube structure, in core
The surrounding setting support of cylinder forms closed support tube, in order to improve the energy dissipation capacity of structure while consider evacuation building door
Hole, A Core Walls Structure support are all designed as accentric support, the central supported of one jiao of setting cross-layer of A outline border.A structure three
Dimension module and inner cylinder support facade are as figs 11-13.
All diagonal braces for planning inner cylinder are replaced using viscous damper, replaced inner cylinder damper 3-D view and facade
View, as illustrated in figures 14-16.
The basic cycle in the direction two main shafts of the model structure (X to, Y-direction) is respectively 5.9974s, 5.7907s, inner cylinder branch
Supportting brace is respectively all 8.1596s, 7.9572s with viscous damper two major axes orientation basic cycles of replaced structure.
According to above method equation (17) as a result, the maximum damping ratio that two major axes orientations of structure can apply be respectively 15.64%,
16.16%.
In addition, according to the above method it is found that being added near maximum damping ratio position in reality, " seismic design provision in building code "
The damping ratio that the 12.3.4 articles method of GB50011-2010 calculates is 2 times of practical maximum damping ratio.Therefore, Midas- is utilized
The strain energy factorization method (as earthquake resistant code recommended method) of Gen is calculated when the damped coefficient of linear dampers is taken as C=
When 300000KN.s/m, the damping ratio of two major axes orientation basic vibration mode of additional structure is about 30% or so, then practical additional resistance
Buddhist nun's ratio should be 15% or so.
So, it when learning linear damping coefficient is C=300000KN.s/m, can obtain in two major axes orientations of structure
Basic cycle additional maximum damping ratio, in actual use in order to reduce maximum output of the damper under rarely occurred earthquake, it will usually
Using Nonlinear Viscous Damper, the Nonlinear Viscous Damper of this proposed adoption damping exponent α=0.2 meets ground according to more
Always consume energy equal principle under shake, linear dampers is scaled nonlinear damper, the nonlinear damper of conversion damps system
Number is C0.2=2500KN. (s/m) 0.2, is applied with 680 Nonlinear Viscous Dampers altogether.
Assuming that encountering earthquake, the wavy curve and fitting spectrum in natural wave L0142 primary and secondary direction are as in figs. 17-19.
At this point, integrality performance of the structure performance comparison is as shown in the table, which provides application and does not apply viscous damper,
Structure maximum story drift, base shear, substrate tilting moment, vertex maximum displacement comparison.
In conjunction with attached drawing 20-25, the comparison of floor maximum relative storey displacement angular curve, floor maximum shear curve distribution pair are given
Than the comparison of, floor maximum tilting moment curve distribution, the comparison of top displacement time-history curves, the comparison of base shear time-history curves, base
The comparison of bottom tilting moment time-history curves.
In conclusion applying the viscous damper of selected damping ratio in the position of selection, meet the requirement of Aseismic Design, no
Necessity carries out the calculating for really applying damper, accurately determines the position for applying viscous damper, greatly reduces
Difficulty in computation during engineering-built in the future.
Based on the various embodiments described above, in conjunction with attached drawing 26, it there is a need to provide and realize viscous damper position in high-level structure
Set determining processing system, comprising:
Standard three-dimensional solid model module 10, including spring K1, spring K2With spring K3*, spring K2With spring K3* after connecting
With spring K1Parallel connection simultaneously supports particle M jointly.
Simulation band viscous damper structural model module 20, spring K3* equivalent transformation is viscous damper.
Additional damping ratio computing module 30, it is enterprising in complex number space based on simulation band viscous damper structural model module
Row operation obtains additional damping ratio algorithm.
Specifically, which carries out calculation process.Wherein, the system of the standard three-dimensional solid model
Under the Simple Harmonic Load P effect that frequency is ω, reciprocating, the simple harmonic quantity of generation is deformed into X, wherein in spring K2With substitution bullet
Spring K3* the simple harmonic quantity deformation generated in viscous damper is respectively Z1And Z2。
On complex number space, the Complex modes K of viscous damper3*=iK3, wherein K3=C ω, i are the symbol of imaginary number, and C is
Damped coefficient.
According to denaturation coordination principle and the equilibrium principle of power, there is following two equation:
Equation (1): X=Z1+Z2
Equation (2): K3*Z1=K2Z2
X and Z are derived in this way2Respectively equal to:
Equation (3): Z2=K3*/K2×Z1
Equation (4): X=Z1×(1+K3*/K2)
The kinetic balance equation that the standard three-dimensional solid model is established on complex number space is as follows:
Equation (5): P=MX "+K1X+K3*Z1
And then it derives:
Equation (6): P=[- ω2M+K1+K2K3*/(K2+K3*)]×X
It derives:
Equation (7): P/X=K1-ω2M+K2K3*/(K2+K3*)
So Complex modes (or equivalent stiffness) of the standard three-dimensional solid model structure are as follows:
Equation (8): Ke=K1+K2K3*/(K2+K3*)
The K known to aforementioned3*=iK3, so:
K2K3*/(K2+K3*)=iK2K3/(K2+iK3)
=K2K3 2/(K2 2+K3 2)+iK2 2K3/(K2 2+K3 2)
The Complex modes (or equivalent stiffness) of the standard three-dimensional solid model structure in this way are as follows:
Equation (9): Ke=K1+K2K3 2/(K2 2+K3 2)+iK2 2K3/(K2 2+K3 2)
So the real part of the Complex modes (or equivalent stiffness) are as follows:
Equation (10): Kr=K1+K2K3 2/(K2 2+K3 2)
So the imaginary part of the Complex modes (or equivalent stiffness) are as follows:
Equation (11): Ki=K2 2K3/(K2 2+K3 2)
According to Structural Dynamics principle, the additional damping ratio (i.e. additional damping ratio algorithm) of the system are as follows:
Equation (12): ζ=Ki/2Ke
=K2 2K3/2/[K1K2 2+K3 2(K1+K2)]
Maximum additional damping ratio computing module 40, to the additional damping ratio algorithm of additional damping ratio computing module it is reciprocal into
Row derivation and minimizing obtain maximum additional damping ratio algorithm.
Specifically, the operation of maximum additional damping ratio computing module be to the operation result of additional damping ratio computing module into
The processing of one step.Specific treatment process is as follows:
The inverse of additional damping ratio algorithm (i.e. equation 12) are as follows:
Equation (13): 1/ ζ=K1/K3+(K1+K2)/K2 2×K3
It is the maximum of ζ that the minimum of 1/ ζ is corresponding, therefore peer-to-peer (13) both sides are to K3Derivation, to acquire 1/ ζ's
Minimum obtains following formula:
Equation (14): d (1/ ζ)/d (K3)=- K1/K3 2+(K1+K2)/K2 2
It is equation (14) is zero that the condition of minimum, which occurs, in 1/ ζ, therefore enables equation (14) to be equal to zero and obtain:
Equation (15): K3 2=K1K2 2/(K1+K2)
By front K3*=iK3It is found that ︳ K3* ︳=K3, therefore:
Equation (16): ︳ K3* ︳=K3=K2×SQRT(K1/(K1+K2))
Enable a=SQRT ((K1+K2)/K1), then K3=K2/ a is rewinded into equation (12), then obtains additional maximum dampingratioζ
Max are as follows:
Equation (17): ζ max=Ki/2Ke
=K2 2K3/2/[K1K2 2+K3 2(K1+K2)]
=K2/a/2/[K1+(K1+K2)/a2]
=(a2-1)/4/a
Maximum damping ratio is calculated by maximum additional damping ratio algorithm in computing module 50.
As can be seen that the maximum damping ratio that viscous damper is applied to system is same viscous damper resistance from equation (17)
Buddhist nun's coefficient is no any relationship, and corresponds to damped coefficient when additional damping ratio reaches maximum (i.e. by C ω=K3=K2/
A derives C=K2/ a/ ω), it utilizes in the 12.3.4 articles of " seismic design provision in building code " GB50011-2010 and its provision explanation
The damping ratio that the formula provided is found out is ζ=(a2- 1)/2/a, 2 times of exactly practical additional damping ratio, it is seen that error is big,
And work as C > K2After/a/ ω, with the increase of C value, error increases in divergence expression.
In addition, further inquiring into a=SQRT ((K1+K2)/K1) physical meaning: assuming that by system shown in Figure 3 in spring
K3* place disconnects, then the natural vibration period of the system is then T1=2 π × SQRT (M/K1)；And by Fig. 3 system in spring K3* place is not with
After the rigid rod connection being deformed, then the natural vibration period of the system is T2=2 π × SQRT (M/ (K1+K2)).Apparent a=
SQRT((K1+K2)/K1)=T1/T2。
Presetting module 60 presets damping target value.Specifically, which can be according to building structure and building
Earthquake intensity region setting where structure.
Viscous damper position computing module 70 adds maximum damping ratio compared with damping target value, obtains viscous resistance
The position of Buddhist nun's device setting.
Further, in conjunction with attached drawing 27, viscous damper position computing module 70 includes:
Natural vibration period, arithmetic element 71, obtained the fundamental natural period of vibration T of standard three-dimensional solid model1。
Arithmetic element natural vibration period 72 is simulated, the position for being used to install viscous damper is connected using rigid rod,
Then fundamental natural period of vibration T of the calculating simulation with viscous damper structural model again2。
Computing unit 73, according to a=T1/T2With maximum dampingratioζ max=(a2- 1) it is viscous that/4/a calculates position setting
Stagnant damper can give structure additional maximum damping ratio.
Comparing unit 74, additional maximum damping ratio judge that additional maximum damping ratio is compared with damping target value
It is no to reach default damping target value, it is the position for obtaining viscous damper setting.
In other embodiments, comparing unit 74 is also used to: determining the not up to default damping of additional maximum damping ratio
Target value, then convert the position of viscous damper, and returns to execution simulation arithmetic element natural vibration period.
In addition, the movement of above-mentioned viscous damper position can be based on following principle: viscous damper position is in structure
Symmetrically it is arranged.The viscous damper being symmetrically arranged can preferably play the function of viscous damper, and help
The target set point of damping is more easily reachd in structure.
In conclusion using the realization viscous damper of this programme processing system that position determines in high-level structure, energy
Enough positions for fast and accurately determining viscous damper, without really applying viscous damper in high building structure
The difficulty calculated during engineering-built greatly reduces in middle tentative calculation.
In one embodiment, stagnant damper usually requires mechanically to connect with structure, and viscous in order to allow
Damper can play very big effect when the deformation of very little occurs for structure.Therefore this programme has determined that viscous damper is placed
Position, then can by the way of being connect as follows with structure, including diagonal strut, herringbone support, elbow formula support or scissors branch
Any one or more in support.
Although describing the present invention with reference to several exemplary embodiments, it is to be understood that, term used be explanation and
Term exemplary, and not restrictive.Due to the present invention can be embodied in a variety of forms without departing from invention spirit or
Essence, it should therefore be appreciated that above embodiment is not limited to any of the foregoing details, and should be defined by the appended claims
The whole change and modification widely explained, therefore fallen into claim or its equivalent scope in spirit and scope all should be with
Attached claim is covered.
Claims (8)
1. a kind of realize the viscous damper processing method that position determines in high-level structure characterized by comprising
Establish standard three-dimensional solid model, the standard three-dimensional solid model includes spring K1, spring K2 and spring K3*, described
Spring K2 is in parallel with the spring K1 after connecting with the spring K3* and supports particle jointly；
It is viscous damper the spring K3* equivalent transformation, then the standard three-dimensional solid model converts to obtain simulation with viscous
Stagnant damper structure model；
Based on the simulation band viscous damper structural model, operation is carried out on complex number space, obtains additional damping ratio algorithm；
Derivation and minimizing are carried out to the reciprocal of the additional damping ratio algorithm, obtain maximum additional damping ratio algorithm；
Maximum damping ratio is calculated by the maximum additional damping ratio algorithm；
Default damping target value；
The additional maximum damping ratio obtains the position of viscous damper setting compared with the damping target value；
The additional maximum damping ratio is with the damping target value compared with, the step of obtaining the position that viscous damper is arranged
Specifically:
Obtain the fundamental natural period of vibration T1 of the standard three-dimensional solid model；
The position for being used to install viscous damper is connected using rigid rod, then calculates the simulation band viscous damping again
The fundamental natural period of vibration T2 of device structural model；
Position setting viscous damper institute is calculated according to a=T1/T2 and maximum dampingratioζ max=(the a2-1)/4/a
It can give structure additional maximum damping ratio；
The additional maximum damping ratio judges whether the additional maximum damping ratio reaches compared with the damping target value
It is the position for obtaining viscous damper setting to the default damping target value.
2. realizing the viscous damper processing method that position determines in high-level structure according to claim 1, feature exists
In, the additional maximum damping ratio with the damping target value compared with, the step of obtaining the position that viscous damper is arranged
Further include:
It determines the additional maximum damping ratio and is not up to the default damping target value, then convert the position of viscous damper
Set, and return execute it is described the position for being used to install viscous damper is connected using rigid rod, then described in the calculating
The step of simulating the fundamental natural period of vibration T2 with viscous damper structural model.
3. realizing the viscous damper processing method that position determines in high-level structure according to claim 2, feature exists
In the additional damping ratio algorithm are as follows: ζ=K22K3/2/ [K1K22+K32 (K1+K2)]；The maximum additional damping ratio algorithm
Are as follows: ζ max=Ki/2Ke；
Wherein, K3=C ω, C are damped coefficient, and ω is frequency, and Ki is the imaginary part of the Complex modes of the standard three-dimensional solid model,
Ke is the Complex modes of the standard three-dimensional solid model.
4. realizing the viscous damper processing method that position determines in high-level structure according to claim 3, feature exists
In the mode that the viscous damper is connect with structure includes: in diagonal strut, herringbone support, the support of elbow formula or scissors support
Any one or more.
5. a kind of realize the viscous damper processing system that position determines in high-level structure characterized by comprising
Standard three-dimensional solid model module, including spring K1, spring K2 and spring K3*, the spring K2 and the spring K3* string
It is in parallel with the spring K1 and support particle jointly after connection；
Simulation band viscous damper structural model module, is viscous damper the spring K3* equivalent transformation；
Additional damping ratio computing module is carried out on complex number space based on the simulation band viscous damper structural model module
Operation obtains additional damping ratio algorithm；
Maximum additional damping ratio computing module carries out the reciprocal of additional damping ratio algorithm of the additional damping ratio computing module
Derivation and minimizing obtain maximum additional damping ratio algorithm；
Maximum damping ratio is calculated by the maximum additional damping ratio algorithm in computing module；
Presetting module presets damping target value；
Viscous damper position computing module, the additional maximum damping ratio obtain viscous compared with the damping target value
The position of damper setting；
Viscous damper position computing module includes:
Natural vibration period, arithmetic element, obtained the fundamental natural period of vibration T1 of standard three-dimensional solid model；
Arithmetic element natural vibration period is simulated, the position for being used to install viscous damper is connected using rigid rod, then again
Fundamental natural period of vibration T2 of the calculating simulation with viscous damper structural model；
It is viscous to calculate position setting according to a=T1/T2 and maximum dampingratioζ max=(the a2-1)/4/a for computing unit
Damper can give structure additional maximum damping ratio；
Comparing unit, the additional maximum damping ratio judge the additional maximum resistance compared with the damping target value
Buddhist nun is the position for obtaining viscous damper setting than whether reaching the default damping target value.
6. realizing the viscous damper processing system that position determines in high-level structure according to claim 5, feature exists
In the comparing unit is also used to: determining the additional maximum damping ratio and be not up to the default damping target value, then become
The position of viscous damper is changed, and returns to execution simulation arithmetic element natural vibration period.
7. realizing the viscous damper processing system that position determines in high-level structure according to claim 6, feature exists
In the additional damping ratio algorithm are as follows: ζ=K22K3/2/ [K1K22+K32 (K1+K2)]；The maximum additional damping ratio algorithm
Are as follows: ζ max=Ki/2Ke；
Wherein, K3=C ω, C are damped coefficient, and ω is frequency, and Ki is the imaginary part of the Complex modes of the standard three-dimensional solid model,
Ke is the Complex modes of the standard three-dimensional solid model.
8. realizing the viscous damper processing system that position determines in high-level structure according to claim 7, feature exists
In the mode that the viscous damper is connect with structure includes: in diagonal strut, herringbone support, the support of elbow formula or scissors support
Any one or more.
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| CN107724527B (en) * | 2017-10-29 | 2019-08-20 | 上海创霖建筑规划设计有限公司 | Frame structure and installation method and design method equipped with viscous damper energy consuming components |
| CN107893562B (en) * | 2017-10-29 | 2020-02-14 | 内蒙古工大建筑设计有限责任公司 | Energy dissipation damper for frame structure |
| CN107916814B (en) * | 2017-10-29 | 2020-02-18 | 郑益丽 | Installation method of energy dissipation damper for frame structure |
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| CN101812879B (en) * | 2010-03-26 | 2012-07-25 | 北京工业大学 | Tuned mass damper for controlling tri-dimensional translation and horizontal torsion of building structure and manufacturing method thereof |
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