CN114329786A - Multi-mode optimization method based on global criterion method constrained damping - Google Patents

Multi-mode optimization method based on global criterion method constrained damping Download PDF

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CN114329786A
CN114329786A CN202111662999.2A CN202111662999A CN114329786A CN 114329786 A CN114329786 A CN 114329786A CN 202111662999 A CN202111662999 A CN 202111662999A CN 114329786 A CN114329786 A CN 114329786A
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袁维东
马俊升
刘伟
李传涛
崔新一
缪国峰
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AVIC Jincheng Nanjing Engineering Institute of Aircraft Systems
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Abstract

The invention discloses a multi-mode optimization method based on global criterion method constrained damping, which comprises the following steps: constructing a finite element model of a laying optimization layer and design variables corresponding to the finite element model and the optimization layer; establishing an interpolation model pseudo-density material library updating unit physical attribute; performing multi-modal structural analysis on the laying structure; utilizing a vibration control factor not less than 0.9; then calculating a relative pseudo-density gradient value of the target function; establishing a universe criterion method to optimize the iteration lattices by adopting an infinite-norm of a heuristic iteration lattice under the condition of optimizing the convexity of the model; and finally, the vibration reduction laying result is optimized in topology under the condition of meeting the constraint condition. The invention provides a convex condition for constructing dynamics topology optimization and designing the whole process of variables to participate in iterative optimization, forms a simple optimization iteration lattice supported by mathematical calculation, avoids the occurrence of local vibration reduction configuration in dynamics, simultaneously provides an iterative gradient formula convenient for updating an interpolation model, and expands the application of working condition frequency width for constructing multi-mode vibration reduction.

Description

Multi-mode optimization method based on global criterion method constrained damping
Technical Field
The invention relates to a damping structure vibration attenuation dynamics optimization method adopting a topological optimization algorithm of a variable density method, belongs to the field of structure dynamics optimization, and particularly relates to a multi-mode optimization method for restraining damping based on a global criterion method.
Background
In the modern aerospace and mechanical engineering fields, structural vibration noise has become a focus of attention. This factor not only affects the characteristics of the design mechanism itself, but also causes reduced stability or accuracy and noise damage to other parts or structures in the vicinity of the structure, and may also cause vibration fatigue to cause an accident in case of a serious accident. The application of viscoelastic damping materials on the surface of structures as a passive vibration reduction technique has been proven to be a practical and effective vibration control measure and has been widely used in recent years. Wherein, the better structure of damping effect is restraint damping structure.
In order to improve the vibration damping force of the structure, the research object is completely covered with viscoelastic damping materials, and the design idea of lightweight aerospace structure is contrary. The topological optimization method is earlier applied to the field of statics, is developed in dynamic vibration reduction, mainly comprises a method of directly applying optimization criteria in statics and a calculation method of neglecting negative values of optimization design variables to participate in iteration, optimizes the sensitivity of an optimization target in a non-negative number range in each iteration process, and reduces an optimization variable area. The progressive method has certain application in dynamic vibration reduction optimization, is established on the basis of physical attributes of units, continuously explores the size of the vibration reduction contribution of the unit cells, selects or rejects the existence of the unit cells to form a vibration reduction topological structure, and can see that the iteration efficiency of an optimized object with more limited units is low. The optimization method is established on the basis of a mathematical theory, parameters in the optimization are changed or added for solving the practical problem in the optimization, mathematical deduction of an iterative formula is needed, and the dynamic application range is conveniently widened. In practical application, the structure is in multi-order mode combined action to cause vibration, and a multi-mode optimization model is not built yet. Moreover, the negative value design variable of the dynamic optimization object does not participate in optimization, and the optimization result of the local extreme point of the optimization criterion method is easy to appear. Meanwhile, the appearance of the optimized extreme value has certain influence on the convexity of the optimized model function.
Disclosure of Invention
The invention aims to provide a multi-mode optimization method based on global criterion method constrained damping, which is used for establishing dynamic vibration reduction optimization of a variable density optimization criterion method of a multi-mode optimization objective function independent of convexity, avoiding unstable changes of positive and negative values of the sensitivity of topological vibration reduction optimization in an optimization iteration process to limit an optimization function to local extreme points and a hopping topological configuration, and establishing multi-mode vibration reduction to widen the application of a working condition frequency domain band on the basis.
In view of the above object, the present invention is achieved by the following means.
A multi-mode optimization method based on global criterion method constrained damping is characterized in that a similarity function is constructed based on a sequence convex planning method in a mathematical programming method, Taylor expansion approximation is established, strict convex conditions of an optimized mathematical model are deduced, and a topological optimization vibration reduction iteration lattice of the global criterion method is constructed on the basis.
Further, the method comprises the following steps:
step 1: establishing a constrained damping structure on the laying surface of the vibration damping object, dividing a finite element method grid, and establishing an optimized design variable corresponding to a constrained layer and a damping layer;
step 2: selecting vibration quantity and multi-modal order which meet the requirement for measuring vibration reduction, determining the boundary condition of a vibration reduction object, optimizing the constrained volume ratio, optimizing the number of units in a design domain, and establishing a multi-modal vibration reduction optimization model of a constrained damping structure;
and step 3: constructing an optimized design variable as a function of the pseudo density quantity of the variable density method and the physical attribute of a vibration damping object of an interpolation model so as to change the unit grid quantity change of a strain quantity rigidity matrix and a mass matrix;
and 4, step 4: adopting multi-mode vibration analysis, establishing tracking analysis of the affected condition of the mode vibration pattern, judging whether the vibration control factor is larger than a preset value, if so, not stepping the mode vibration pattern, executing the step 5, otherwise, adjusting a vibration reduction object physical attribute function of the interpolation model, and repeatedly executing the steps 1-3, wherein the vibration control factor is larger than the preset value;
and 5: calculating the iteration direction gradient of the optimization objective function relative to the design variable;
step 6: constructing a similarity function based on a sequence convex planning method in a mathematical planning method, deriving a strict convexity condition of an optimized mathematical model, constructing a global criterion method optimized iteration lattice, and updating an optimized design variable pseudo density;
and 7: and (3) establishing criteria to determine convergence by adopting the optimized design variables before and after iteration updating, finishing optimization if the convergence conditions are met, otherwise, continuing optimization iteration, repeating the steps 3 to 6, finally meeting the criteria conditions, and analyzing the harmonic response of the topological structure.
Further, the constrained damping structure multi-modal vibration attenuation optimization model in the step 2 is divided into a Fi nd model and a Mi n model, and the constrained conditions between the Fi nd model and the Mi n model are as follows:
Figure BDA0003447755410000031
wherein, χnInterpolating the pseudo density of the model for the nth unit and taking the pseudo density as an optimization design variable; x is a design variable vector; Ψ is an optimization objective function;
Figure BDA0003447755410000032
the weight coefficient for the ith-order multi-modal optimization can be selected according to actual needs, and the value of the weight coefficient is positive; s.t is a constraint condition between the Fi nd model and the Min model, and V is the volume of a damping layer of a vibration damping object; r is the optimized volume ratio of the vibration damping object; TN is the total number of the optimization design variables;
sn、hnare respectively unit areaAnd a cell height; v0The total full laying volume of the damping layer and the constraint layer is provided; chi shapemin、χmaxThe minimum value and the maximum value of the optimization design variable are expressed, and 0.001 and 1.0 can be respectively selected; the moving constant is A in the iterative optimization solution.
Further, the physical property function of the object to be damped of the interpolation model described in the step 3 is I (χ)n) Expressed as having a pseudo-density value χnWhen the value tends to 0, the high order of the value tends to 0; when the pseudo density value χnWhen the value of the signal tends to 1, the value tends to 1 infinitely.
Further, the global criterion method for optimizing the iteration lattice in step 6 ensures that the multi-modal optimization model has strict convexity condition, and the specific steps are as follows when the lagrangian optimization function extremum condition is required to be met:
constructing a Lagrange multiplier method formula of a vibration reduction optimization model; calculating a similarity function approximation formula by using a Taylor series expansion formula; and deducing the numerical relation of the moving parameters in the similarity function according to the strict convex similarity function condition.
Further, under the condition of satisfying the extreme value of the Lagrange optimization function, the numerical relation of the mobile parameters in the similar function has
Figure BDA0003447755410000041
Wherein when
Figure BDA0003447755410000042
The objective function is strictly convex.
Further, a parameter c in the k-th iteration may be establishedkExpressed in an ∞ -norm: c. Ck＝||Qk||∞And is and
Figure BDA0003447755410000043
further, the global criterion method optimizes the iteration lattice as
Figure BDA0003447755410000044
And the number of the first and second electrodes,
Figure BDA0003447755410000045
wherein zeta is a convex function construction index, lambda is a design variable movement limit value, and the value range of lambda is 0-1; k is the number of iterations.
Further, the moving constant is A, and A is equal to or more than etaiForming a minimum value positive value change process in objective function value iterative optimization; the weight coefficients of the multi-modal optimization
Figure BDA0003447755410000046
The numerical values are non-negative numbers.
Further, the physical property function of the vibration damping object comprises Young's modulus E of elasticity of the damping material0And density ρ0The unit grid deformation of the strain stiffness matrix and the mass matrix is set up and has E (x)n)＝I1(χn)·E0、ρ(χn)＝I2(χn)·ρ0。
The invention has the advantages that: in a wide frequency domain, a multi-mode optimization model vibration attenuation topological optimization is established, a constraint damping structure in a passive vibration attenuation structure is adopted, a finite element numerical analysis method is applied, and the topological configuration of the vibration attenuation position where the viscoelastic material is laid is optimized based on the variable density method topological optimization theory, so that the lightweight design requirement of meeting the vibration attenuation dynamics requirement is met. And constructing a similarity function based on a sequential convex programming method in a mathematical programming method, and deducing a numerical relation of the mobile parameters in the similarity function according to strict convex similarity function conditions. On the basis, the global optimization iteration algorithm enables all unit design variables in the object optimization domain to participate in the whole optimization iteration process, and through constructing strict conditions of convexity, unified convexity expression conditions, namely infinity-norm expressions, of the design variables of different optimization objective functions are formed. Meanwhile, an operable global criterion method is formed to optimize iteration grids, the parameter setting of the formula is improved to be simple, different iteration grid formula forms are established in a classified mode, the occurrence of dynamic vibration reduction optimization local configuration is finally avoided, compared with the traditional method, the sensitivity threshold value setting in the optimization criterion method formula has a basis, and the stability of an iteration optimization area is improved.
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FIG. 1 is a flow chart of a multi-modal topology optimization with damping constrained by a global criteria method;
FIG. 2 is a schematic diagram of a finite element model of a constrained damping structure on a laying surface of a vibration damping object;
FIG. 3 is a graph of an iteration process of a multi-modal topology optimization objective function with damping constrained by a global criterion method;
FIG. 4 is a multi-modal topology optimization topology harmonic analysis;
FIG. 5 is a 1 st order modal topology optimization objective function iteration process diagram of the global criterion method constrained damping;
FIG. 6 is a harmonic analysis of a 1-order modal topology optimization topology configuration;
FIG. 7 is a graph of an iteration process of a 2 nd order modal topology optimization objective function with global criterion method constrained damping;
FIG. 8 is a harmonic analysis of a 2-order modal topology optimization topology configuration;
FIG. 9 is a 3-order modal topology optimization objective function iteration process diagram of the global criterion method constrained damping;
FIG. 10 is a harmonic analysis of a 3 rd order modal topology optimization topology configuration.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other and the parameters may be changed within the range as long as they do not conflict with each other.
The first embodiment is as follows:
referring to fig. 1 and fig. 2, an embodiment of a multi-modal optimization method design based on the global criteria constrained damping is as follows: the shell-plate connection structure of the component with wide requirements in engineering is adopted, the length L of the plate is 0.55m, the width D is 0.25m, the radius R of the shell is 1mm, and the angle theta of the rotation is 30 degrees. The restraint damping structure: thickness of base materialDegree of 3mm, Young's modulus of elasticity of 43.2GPa, Poisson's ratio of 0.33, density of 1810Kg/m3(ii) a The Young's modulus of the damping layer material is 15MPa, and the density is 1550Kg/m3The Poisson ratio is 0.5, the material loss factor is 0.75, and the paving thickness is 1 mm; the constraining layer is in conformity with the base layer. The optimization method comprises the following design steps:
step 1: establishing a constrained damping structure on the laying surface of the vibration damping object, dividing a finite element grid, and establishing an optimized design variable corresponding to a constrained layer and a damping layer;
step 2: selecting vibration quantity eta for measuring vibration reduction meeting requirementsiThe modal loss factor and the multi-modal order r are the first 3 orders, the boundary condition of a vibration damping object is unilateral long edge fixed constraint, an excitation point and an extraction point of harmonic response analysis are set, the optimized constraint volume ratio gamma is set to be 0.5, the number n of units in an optimized design domain is 3480, and a multi-modal vibration damping optimization model of a constrained damping structure is established;
and step 3: constructing an optimized design variable as a vibration damping object physical attribute function I (x) of a pseudo density quantity and interpolation model of a variable density methodn) Changing the unit grid quantity change of the strain quantity rigidity matrix and the mass matrix;
and 4, step 4: extracting strain energy SE of finite element in optimized domain by adopting finite element model multi-modal vibration analysiseiKinetic energy KEeiEstablishing the tracking analysis of the influence of the original structure mode vibration mode on the original structure mode vibration mode, and meeting the requirement of a vibration control factor
Figure BDA0003447755410000061
And 5: calculating an iterative directional gradient of an optimization objective function relative to a design variable
Figure BDA0003447755410000062
Step 6: constructing a similarity function based on a sequence convex planning method in a mathematical planning method, deriving and optimizing strict convexity conditions of a mathematical model, constructing a global criterion method optimization iteration lattice, and updating an optimized design variable pseudo density
Figure BDA0003447755410000063
And 7: establishing criterion eta by adopting optimized design variables before and after iterative updatek+1-ηkAnd determining the convergence property if the | is less than or equal to 0.001. If the convergence condition is met, finishing the optimization, otherwise, continuing the optimization iteration, and repeating the steps 3 to 6 to finally meet the criterion condition. And analyzing the topological structure harmonic response.
Further, the constrained damping structure multi-modal vibration damping optimization model in step 2:
Figure BDA0003447755410000064
wherein X is a design variable vector; chi shapenInterpolating the pseudo density of the model for the nth unit and taking the pseudo density as an optimization design variable; Ψ is an optimization objective function;
Figure BDA0003447755410000071
weight coefficients optimized for multiple modalities; sn、hnCell area and cell height, respectively; v0Constraining the volume of the damping layer for the modeled vibration damping object; chi shapemin、χmaxThe minimum value and the maximum value of the optimization design variable are expressed, and 0.001 and 1.0 can be respectively selected; TN is an optimized area constrained damping finite element number 3480; the moving constant is A in the iterative optimization solution.
Furthermore, the weight coefficient of the multi-modal optimization in the multi-modal vibration attenuation optimization model of the constrained damping structure
Figure BDA0003447755410000079
Controlling different modes gives priority and emphasis on the selection of natural frequency region damping effects in damping optimization. In the starting process of the mechanism, the ratio of the first few-order modes is high, and the ratio of the weight coefficients of the multi-mode optimization of the first 3-order modes is 1:1: 1.
Further, the interpolation model function I (χ) in step 3n) Expressed as having a pseudo-density value χnWhen the value tends to 0, the high order of the value tends to 0; when it is falseDensity value χnWhen the value of the signal tends to 1, the value tends to 1 infinitely. The embodiment selects the interpolation function with wider common application
Figure BDA0003447755410000072
And wherein the independent variables are optimization parameters;
further, the physical property function of the vibration damping object comprises Young's modulus E of elasticity of the damping material0And density ρ0The unit grid quantity deformation of the strain quantity rigidity matrix and the mass matrix is set up by
Figure BDA0003447755410000073
Further, in the multi-modal vibration analysis in the step 4, a structural modal loss factor eta is established by adopting modal strain energyi；
Further, said strain energy, single target ηiIn relation to it
Figure BDA0003447755410000074
Wherein eta isνThe loss factor of the viscoelastic layer material is a value which changes along with the working temperature and frequency in a certain range;
Figure BDA0003447755410000075
respectively representing i-order modal strain energy of the damping layer and the non-damping layer;
Figure BDA0003447755410000076
i-order modal total strain energy of the composite shell structure.
Further, the iterative direction gradient described in step 5 is expressed by
Figure BDA0003447755410000077
Figure BDA0003447755410000078
Wherein, KEei、SEeiThe current i-order modal kinetic energy and modal strain energy of a certain iteration unit are respectively; i is1′(χn)、I2′(χn) Interpolating the first derivative of the model for the material to be
Figure BDA0003447755410000081
Further, the global criterion method for optimizing the iteration lattice in step 6 ensures that the multi-modal optimization model has strict convexity condition, and the specific steps are as follows when the condition of the extreme value of the lagrangian optimization function needs to be met:
1) lagrange multiplier method formula for constructing optimization model
Figure BDA0003447755410000082
Wherein, Λ and β-n、β+nAre all lagrange multipliers;
2) similarity function approximation formula is calculated by using Taylor series expansion formula
Figure BDA0003447755410000083
Wherein, the shift parameter c is introduced to let psi-cV become psi*，Λ＝Λ*-c，yn＝(1/χn)ζ；
3) Deducing the numerical relation of the mobile parameters in the similarity function according to the strict convex similarity function condition
Figure BDA0003447755410000084
Further, on the basis of the convexity condition, heuristic iterative lattice derivation is adopted to determine the movement parameter ckI.e. by
Figure BDA0003447755410000085
Wherein when
Figure BDA0003447755410000086
The objective function is strictly convex.
Further, it explicitly leads to
Figure BDA0003447755410000087
The parameter c in the k iteration can be establishedkExpressed in an ∞ -norm: c. Ck＝||Qk||∞And vector
Figure BDA00034477554100000811
Further, heuristic iterative derivation is definitely adopted, and a universe rule method is adopted to optimize an iteration lattice into
Figure BDA0003447755410000089
Wherein the content of the first and second substances,
Figure BDA00034477554100000810
wherein k is iteration number, zeta is convex function construction index less than 0, lambda (0)<λ<1) The moving limit value of the design variable can be 0.3 and is an optimization parameter.
Further, the movement constant of the constrained damping structure multi-modal vibration attenuation optimization model in the step 2 is A, and A is required to be larger than or equal to etaiAnd forming a minimum value positive value change course in the iterative optimization of the objective function value. Therefore, the moving constant A is 1 without loss of generality.
Fig. 3 is a diagram for optimizing an iteration change process of the target function topological structure, which reflects that the optimization range is large and stable topological structure appears fast in iteration. The change before and after the first three-order natural frequency optimization is within 3 Hz; meanwhile, when the laying volume is less than 50%, the change of the modal loss factor is not more than 0.05, and the topological vibration reduction optimization for reducing the volume of the laid damping material on the premise of not influencing the vibration reduction effect is achieved.
Example two:
the second embodiment is a preferred embodiment of the first embodiment, and is different from the first embodiment in that the weighting coefficients of the multi-modal optimization in the multi-modal topology optimization of the vibration damping object are displayed in a classified change manner, so that the application range is widened.
Weight coefficient for multi-modal optimization in building multi-modal vibration attenuation optimization model of constrained damping structure
Figure BDA0003447755410000091
Can take different values in practical application and meet the requirements
Figure BDA0003447755410000092
The optimization objective function constructed by the multi-modal optimization method has the characteristic of single-modal optimization when each order of modal emphasis vibration reduction optimization is carried out. The weighting factors are given in the table below
Figure BDA0003447755410000093
Different values assigned in the previous 3-order modal damping optimization reflect the advantages of both single mode and multi-mode. Weight coefficients in unimodal optimization
Figure BDA0003447755410000094
The value is assigned to be 1, which represents that the vibration reduction requirement under the condition of light weight constraint is only improved for a specific certain order of mode; weight coefficient
Figure BDA0003447755410000095
The value is assigned to be 0, which indicates that the vibration reduction optimization is not carried out; weight coefficient
Figure BDA0003447755410000096
The assignment ratio is 1:1:1, the modes of all orders are treated in the same position, and the vibration reduction optimization effects are balanced mutually.
Figure BDA0003447755410000097
The corresponding modal loss factor in the table can be seen. It can be found that: the optimized restraint body is 50%, and single-order optimization is increased, but the increase amplitude is small and is not more than 3.8%; in the multi-mode optimization, the first-order modal loss factor and the second-order modal loss factor are increased, and the third order loss factor is reduced by 1%. Overall, the modal loss factor of the stable topology is slightly upward. However, from the frequency perspective, each order of optimization has a drop, which does not exceed 5%, keeping the frequency almost unchanged. Fig. 5, fig. 7 and fig. 9 show the iterative process of the optimization function of the single-order shell-plate connection structure, the initial stage of the iteration shows a descending trend, then the intermediate value of the pseudo density value becomes smaller, the intermediate value gradually tends to two stages, and the curve rising finally tends to be stable. The curves of fig. 6 represent the first order optimized harmonic response analysis, and fig. 8 and 10 represent the second and third order optimized harmonic response analyses, both reflecting that the harmonic response excitation amplitude is comparable to the full coverage constrained damping layer effect under the constraint of 50% by volume. However, fig. 4 shows a multi-modal optimized harmonic response curve, and different orders of modes have good vibration suppression effect, and meanwhile, the optimization results of modal loss factors with different weights in the table are verified.
In a preferable scheme, the method can not only fully consider modal loss factors as vibration measurement indexes, but also select other researched vibration parameters to determine the laying position of the topology optimization viscoelastic material by combining vibration theory knowledge, and can also change the physical attribute functions of the vibration reduction objects of different interpolation models.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A multi-mode optimization method based on global criterion method constrained damping is characterized in that: and constructing a similarity function based on a sequential convex programming method in a mathematical programming method, establishing Taylor expansion approximation, deriving and optimizing strict convexity conditions of a mathematical model, and constructing a topological optimization vibration reduction iteration lattice of a global criterion method on the basis.
2. The multi-modal optimization method based on the global criteria constrained damping of claim 1, wherein: the method comprises the following steps:
step 1: establishing a constrained damping structure on the laying surface of the vibration damping object, dividing a finite element method grid, and establishing an optimized design variable corresponding to a constrained layer and a damping layer;
step 2: selecting vibration quantity and multi-modal order which meet the requirement for measuring vibration reduction, determining the boundary condition of a vibration reduction object, optimizing the constrained volume ratio, optimizing the number of units in a design domain, and establishing a multi-modal vibration reduction optimization model of a constrained damping structure;
and step 3: constructing an optimized design variable as a function of the pseudo density quantity of the variable density method and the physical attribute of a vibration damping object of an interpolation model so as to change the unit grid quantity change of a strain quantity rigidity matrix and a mass matrix;
and 4, step 4: adopting multi-mode vibration analysis, establishing tracking analysis of the affected condition of the mode vibration pattern, judging whether the vibration control factor is larger than a preset value, if so, not stepping the mode vibration pattern, executing the step 5, otherwise, adjusting a vibration reduction object physical attribute function of the interpolation model, and repeatedly executing the steps 1-3, wherein the vibration control factor is larger than the preset value;
and 5: calculating the iteration direction gradient of the optimization objective function relative to the design variable;
step 6: constructing a similarity function based on a sequence convex planning method in a mathematical planning method, deriving a strict convexity condition of an optimized mathematical model, constructing a global criterion method optimized iteration lattice, and updating an optimized design variable pseudo density;
and 7: and (3) establishing criteria to determine convergence by adopting the optimized design variables before and after iteration updating, finishing optimization if the convergence conditions are met, otherwise, continuing optimization iteration, repeating the steps 3 to 6, finally meeting the criteria conditions, and analyzing the harmonic response of the topological structure.
3. The multi-modal optimization method based on the global criteria constrained damping of claim 2, wherein: the constrained damping structure multi-modal vibration attenuation optimization model in the step 2 is divided into a Find model and a Min model, and the constrained conditions between the Find model and the Min model are as follows:
Figure FDA0003447755400000021
wherein, χnInterpolating the pseudo density of the model for the nth unit and taking the pseudo density as an optimization design variable; x is a design variable vector; Ψ is an optimization objective function; thetaiThe weight coefficient for the ith-order multi-modal optimization can be selected according to actual needs, and the value of the weight coefficient is positive; s.t is a constraint condition between the Find and the Min model, and V is the volume of a damping layer of a vibration damping object; r is the optimized volume ratio of the vibration damping object; TN is the total number of the optimization design variables;
sn、hncell area and cell height, respectively; v0The total full laying volume of the damping layer and the constraint layer is provided; chi shapemin、χmaxThe minimum value and the maximum value of the optimization design variable are expressed, and 0.001 and 1.0 can be respectively selected; the moving constant is A in the iterative optimization solution.
4. The multi-modal optimization method based on the global criteria constrained damping of claim 2, wherein: the physical property function of the vibration damping object of the interpolation model in the step 3 is I (x)n) Expressed as having a pseudo-density value χnWhen the value tends to 0, the high order of the value tends to 0; when the pseudo density value χnWhen the value of the signal tends to 1, the value tends to 1 infinitely.
5. The multi-modal optimization method based on the global criteria constrained damping of claim 2, wherein: the global criterion method for optimizing the iteration lattice in the step 6 ensures that the multi-mode optimization model has strict convexity condition and needs to meet the Lagrange optimization function extremum condition, and the specific steps are as follows:
constructing a Lagrange multiplier method formula of a vibration reduction optimization model; calculating a similarity function approximation formula by using a Taylor series expansion formula; and deducing the numerical relation of the moving parameters in the similarity function according to the strict convex similarity function condition.
6. The multi-modal optimization method based on the global criteria constrained damping of claim 5, wherein: under the condition of satisfying the extreme value of the Lagrange optimization function, the numerical relation of the mobile parameters in the similar function has
Figure FDA0003447755400000031
Wherein when
Figure FDA0003447755400000032
The objective function is strictly convex.
7. The multi-modal optimization method based on the global criteria constrained damping of claim 6, wherein: the parameter c in the k iteration can be establishedkExpressed in an ∞ -norm: c. Ck＝||Qk||∞And is and
Figure FDA0003447755400000033
8. a multi-modal optimization method based on global criteria constrained damping according to claim 5 or 6, characterized in that: the global rule method optimizes the iteration lattice as
Figure FDA0003447755400000034
And the number of the first and second electrodes,
Figure FDA0003447755400000035
wherein zeta is a convex function construction index, lambda is a design variable movement limit value, and the value range of lambda is 0-1; k is the number of iterations.
9. The multi-modal optimization method based on the global criteria constrained damping of claim 3, wherein: what is needed isThe moving constant is A, and A is equal to or greater than etaiForming a minimum value positive value change process in objective function value iterative optimization; the weight coefficient theta of the multi-modal optimizationiThe numerical values are not negative numbers.
10. The multi-modal optimization method based on the global criteria constrained damping of claim 4, wherein: the physical property function of the vibration damping object comprises the Young modulus E of the damping material0And density ρ0The unit grid deformation of the strain stiffness matrix and the mass matrix is set up and has E (x)n)＝I1(χn)·E0、ρ(χn)＝I2(χn)·ρ0。
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Publication number Priority date Publication date Assignee Title
CN116976121A (en) * 2023-08-02 2023-10-31 中国长江三峡集团有限公司 Constrained damping wind power tower and parameter optimization method thereof
CN116976121B (en) * 2023-08-02 2024-05-14 中国长江三峡集团有限公司 Constrained damping wind power tower and parameter optimization method thereof

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