CN112434427B - Vibration-proof structure dynamics optimization design method - Google Patents

Vibration-proof structure dynamics optimization design method Download PDF

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CN112434427B
CN112434427B CN202011345761.2A CN202011345761A CN112434427B CN 112434427 B CN112434427 B CN 112434427B CN 202011345761 A CN202011345761 A CN 202011345761A CN 112434427 B CN112434427 B CN 112434427B
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丁晓红
沈磊
张横
胡天男
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University of Shanghai for Science and Technology
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Abstract

The invention relates to a vibration-proof structure dynamics optimization design method, which comprises the following steps: 1. initializing a design model and defining optimization parameters; 2. carrying out modal analysis on the engineering structure without the damper; 3. optimally tuning a damper; 4. analyzing the structural harmonic response and the design sensitivity of the damper; 5. and optimizing the layout of the engineering structure rib plate based on the self-adaptive growing method. And 2-5, repeating optimization circulation, wherein in each circulation, the position and damping parameters of the damper and the rib plate layout of the structure are updated, and the optimization program is ended until the iteration termination condition is reached. By simultaneously carrying out optimization design on the engineering structure and the damper, the dynamic performance of the engineering structure is obviously improved due to the consideration of the mutual effects of the layout of the rib plates of the engineering structure, the position of the damper and the damping parameters of the damper.

Description

Vibration-proof structure dynamics optimization design method
Technical Field
The invention relates to a dynamic design method of an anti-vibration structure, in particular to a simultaneous optimization design method aiming at the layout of internal rib plates of an engineering structure and a tuned mass damper (hereinafter referred to as a damper).
Background
The three-dimensional engineering structure with the reinforcing ribs inside is widely applied to the fields of aerospace, ships, mechanical engineering, civil engineering and the like, the structures can bear vibration caused by dynamic loads, and the improvement of the anti-vibration performance of the structures through structural optimization design has great significance. The rib plate layout optimization design (topology optimization) and the reasonable arrangement of the dampers are effective anti-vibration design methods, and the two methods can respectively improve the dynamic performance of the engineering structure from two angles of rigidity and damping.
At present, the application and research of the two aspects are separated independently, and the design research is generally carried out from only one aspect. However, the two have obvious interaction relationship, that is, the layout form of the rib plate of the engineering structure affects the optimal layout position and damping parameters of the damper, and in turn, the layout of the damper also affects the layout of the rib plate of the engineering structure. The engineering structure and the damper are optimally designed and combined with each other, and the anti-vibration capability of the engineering structure can be further improved by simultaneously optimally designing.
Disclosure of Invention
The invention provides an anti-vibration structure dynamics optimization design method, which is a method for simultaneously optimizing and designing the layout of rib plates and auxiliary dampers of an engineering structure, and the method comprises the steps of optimizing the layout of the rib plates of the engineering structure (level 1) and optimally tuning the dampers (level 2) by introducing a multi-level optimization strategy, and updating the positions and damping parameters of the dampers in the rib plate layout optimization iteration step of each engineering structure so as to fully consider the interaction between the rib plate layout of the engineering structure and the optimal tuning of the dampers.
The technical scheme of the invention is as follows: an optimization design method for anti-vibration structure dynamics comprises a design method for simultaneously optimizing rib plate layout and an auxiliary damper of a three-dimensional engineering structure, and an adopted optimization mathematical model is as follows:
Figure BDA0002799869690000021
the design variables include: rib thickness T ═ T of engineering structure1,T2,…Tn]Stiffness k of the damperD＝[k1,k2,…,kN]And damping cD＝[c1,c2,…,cN]Position p of damper ═ p1,p2,…,pN]N and N are respectively the number of the rib plate units and the dampers, and the optimization aim is to minimize the dynamic flexibility of the engineering structure in the frequency domain
Figure BDA0002799869690000022
Calculated from the following formula:
Figure BDA0002799869690000023
wherein J (omega) is the dynamic flexibility of the engineering structure when the excitation frequency is omega0Is the upper limit of the excitation frequency range;
equation 1(c) is the modal balance equation (damper-free) for an engineering structure, with the purpose of determining the position of the damper; formula (II)1(d) volume constraints for the engineered structure, v and v0Respectively representing the actual volume and the initial volume of the engineering structure, wherein eta is the volume fraction of the engineering structure; equations 1(e) - (h) are upper and lower limit constraints for design variables, kminAnd kmaxRespectively the minimum value and the maximum value of the rigidity of the damper; c. CminAnd cmaxRespectively the minimum value and the maximum value of the damping; in formula 1(h), N0Represents the maximum number of nodes of the engineering structure in the finite element model, which means the position p of the damperjCan be positioned on any node of the engineering structure in the finite element model;
the method comprises the following design steps:
1. initializing a design model, and defining optimization parameters;
2. carrying out modal analysis on the engineering structure without the damper;
3. optimal tuning of the damper, namely determining the optimal position and damping parameters of the damper: setting a target mode, namely the maximum mode displacement position of a mode needing vibration reduction as the position of the damper arrangement, then arranging the damper at the position, and optimizing the damping parameters of the damper by adopting an SQP sequence quadratic programming algorithm, wherein an optimized mathematical model is as follows:
Figure BDA0002799869690000031
in the formula, JmaxThe maximum dynamic flexibility of the engineering structure in the target mode. k is a radical ofjAnd cjIs the stiffness and damping of the jth damper. Their initial values are calculated by the following formula:
Figure BDA0002799869690000032
wherein m is0Being the mass of the damper, ωMFor the natural frequency of the engineered structure in the target mode, μ is the mass ratio of the damper to the engineered structure, determined by:
Figure BDA0002799869690000033
wherein ω is0Is the natural frequency of the damper0The modal mass for an engineered structure is calculated by:
Figure BDA0002799869690000034
wherein ω'MIs to add a mass m at the maximum modal displacement0Behind the mass of (a), the engineered structure is at the natural frequency of the target mode.
By the method, the optimal tuning parameters of the damper can be obtained, and when the convergence condition of the SQP algorithm is met, the optimization program exits the optimal tuning process of the damper;
4. harmonic response analysis and design sensitivity analysis of the damper-containing structure: establishing a finite element model of an engineering structure-damper system, obtaining the dynamic flexibility of the engineering structure in a frequency domain through harmonic response analysis, regarding the dynamic flexibility as an optimization target, and then carrying out design variable: thickness T of rib platehThe following formula is adopted for the analytical calculation of the sensitivity of (1):
Figure BDA0002799869690000035
wherein
Figure BDA0002799869690000036
And
Figure BDA0002799869690000037
a stiffness matrix and a mass matrix, u, divided into engineering structural unitseA displacement matrix that is a cell;
5) optimizing the layout of the rib plates by adopting a self-adaptive growing method to obtain a new engineering structure model; the self-adaptive growth method is based on the growth rule of a natural branch system, and for a box-type structure reinforcing rib structure, the rib plate can grow, diverge and degenerate according to a certain criterion from a seed line to finally obtain the optimal rib plate layout form;
and 2) repeatedly optimizing and circulating, wherein in each circulation, the position and the damping parameters of the damper and the rib plate layout of the engineering structure are updated until an iteration termination condition is reached, and the optimization program is ended.
The invention has the beneficial effects that:
the invention has the advantages that the prior optimization design method usually only optimizes the topology of the structure, or the structure is kept unchanged, only optimizes the arranged damper, and does not combine the optimization design of the structure and the damper. By simultaneously optimizing the engineering structure and the damper, the dynamic performance of the engineering structure is obviously improved.
Drawings
FIG. 1 is a flow chart of an optimization design method of the present invention;
FIG. 2 is a method of constructing a box model based structure;
wherein: (a) adopting a hexahedral discrete box-type structure, (b) rib plates in the hexahedral structure, and (c) a geometric model of a base structure;
FIG. 3 is a box-type structural model for use in the design of the present invention;
wherein: (a) as a design object, (b) as a constructed base structure;
FIG. 4 is a design flow of an adaptive growth method;
wherein: (a) for designing the model, (b) to (e) are the growth process of the rib plate: wherein (b) the initial growth stage (the growth of the rib plates starts from the seed line), (c) to (d) the growth and the degeneration of the rib plates, and (e) the final layout form of the rib plates;
FIG. 5 is a process of computational simultaneous optimization design of the present invention;
wherein: (a) IN ═ 1, (b) IN ═ 4, (c) IN ═ 11, (d) IN ═ 45 (final), (e) top view;
FIG. 6 is an optimization result obtained by the present invention;
wherein: (a) optimizing an iteration curve, and (b) obtaining a dynamic flexibility curve;
FIG. 7 is a comparison of the dynamic performance obtained by the present invention and a conventional non-simultaneous optimization method.
Detailed Description
In particular, the described embodiments are merely exemplary of the invention, rather than all exemplary. All other embodiments, which can be derived by an engineer skilled in the art from the embodiments described in the present invention before the innovative invention is made, belong to the scope of protection of the present invention.
The embodiment is directed at a common three-dimensional engineering structure, and the anti-vibration performance of the structure is improved through the layout design of the reinforcing ribs of the three-dimensional box type structure. For the simultaneous optimization design method of rib plate layout and damper of the three-dimensional box-type structure, the adopted optimization mathematical model is as follows:
Figure BDA0002799869690000051
wherein T ═ T1,T2,…Tn]Is the set of rib plate thicknesses, kD＝[k1,k2,…,kN]And cD＝[c1,c2,…,cN]The stiffness and the damping of the damper are respectively integrated, and N and N are respectively the number of rib plate units and the number of the dampers. p ═ p1,p2,…,pN]And (4) numbering a set of box-type structure surface nodes in the finite element model to represent the position of the damper. The optimization objective is to minimize the dynamic compliance of the engineered structure in the frequency domain
Figure BDA0002799869690000052
Calculated from the following formula:
Figure BDA0002799869690000053
wherein J (omega) is the dynamic flexibility of the engineering structure when the excitation frequency is omega0The upper limit of the excitation frequency range. Equation 8(c) is a box-type structure modal balance equation (no damper) for the purpose of determining the position of the damper.Equation 8(d) represents the volume constraint of the box-type structure, v and v0The actual volume and the initial volume of the box type structure are respectively represented, and eta is the volume fraction of the engineering structure. Equation 8(e-h) is a constraint on the upper and lower limits of the design variables. k is a radical ofminAnd kmaxRespectively the minimum value and the maximum value of the rigidity of the damper; c. CminAnd cmaxRespectively the minimum and maximum value of the damping. In formula 8(h), N0The maximum number of nodes of the surface of the box-type structure in the finite element model is shown. This means the position p of the damperjCan be positioned on any node of the surface of the box structure in the finite element model.
As shown in fig. 1, a method for simultaneously optimizing layout of rib plates of box-type structure and design of a damper includes, but is not limited to, the following steps:
1. the method for establishing the base structure of the box model is shown in FIG. 2. Discretely dividing the box-type model into hexahedral units, and constructing a shell unit with a certain thickness on the surface of the model according to the node information, as shown in fig. 2 (a), for representing a panel of the box-type structure; then, constructing an internal shell unit along a certain projection direction according to the node coordinates to represent the rib plate, as shown in (b) of FIG. 2; the resulting overall base structure model is shown in fig. 2 (c). The panel of box structure is the non-design domain, and inside gusset is the design domain, and the initial thickness of inside gusset is very little, can ignore the influence to the performance of model. The hexahedral cells are excluded from subsequent analysis and optimization, leaving only the shell cells. The constructed base structure for the design object shown in fig. 3 (a) is shown in fig. 3 (b).
2. The damper is optimally tuned. In the cycle of tuning the damper, firstly, modal analysis (without damper) needs to be performed on the box-type structure, and then the maximum modal displacement position of the target modal (the modal needing vibration reduction) is set as the position of the damper arrangement, because the modal mass at the position with the maximum modal displacement is larger, and the damper can exert better damping performance. Then installing a damper at the position, and optimizing damping parameters of the damper by adopting an SQP (sequential quadratic programming) method, wherein an optimized mathematical model is as follows:
Figure BDA0002799869690000061
in the formula, JmaxThe maximum dynamic flexibility of the box-type structure in the target mode is obtained. k is a radical ofjAnd cjIs the stiffness and damping of the jth damper. Their initial values are calculated by the following formula:
Figure BDA0002799869690000062
wherein m is0Being the mass of the damper, ωMμ is the mass ratio of the damper to the box-type structure, determined by the following equation:
Figure BDA0002799869690000063
wherein ω is0Is the natural frequency of the damper. M (mum)0The modal mass of an engineered structure is determined by:
Figure BDA0002799869690000071
wherein ω'MIs to add a mass m at the maximum modal displacement0Behind the mass of the engineered structure, the natural frequency of the target mode of the engineered structure.
By the method, the optimal tuning parameters of the damper are obtained. When the convergence condition of the SQP algorithm is met, the optimization program exits the optimal tuning process of the damper.
3. And (3) analyzing harmonic response and design sensitivity of the damper-containing structure. And establishing a finite element model of the box-type structure-damper system, and obtaining the dynamic flexibility of the box-type structure in a frequency domain through harmonic response analysis, wherein the dynamic flexibility is regarded as an optimization target. Then, design variables (rib plate thickness T)h) The following formula is adopted for the analytical calculation of the sensitivity of (1):
Figure BDA0002799869690000072
wherein
Figure BDA0002799869690000073
And
Figure BDA0002799869690000074
a stiffness matrix and a mass matrix, u, of the h-th ribeIs a displacement matrix of the rib plate.
4. And optimizing the layout of the rib plates by adopting a self-adaptive growing method to obtain a new box type structure model. The adaptive growth method is based on the growth rule of the natural branch system, and the design flow is shown in fig. 4. For the box-type structure reinforcing rib structure, as shown in fig. 4 (a), the rib plates can start from a seed line, as shown in fig. 4 (b), and grow, diverge and degenerate according to the growth rule of a specific plant branching system, as shown in fig. 4 (c) to (d), and finally obtain the optimal rib plate layout, as shown in fig. 4 (e), and the performance of the box-type structure is also optimal.
And 2-4, repeating optimization circulation, wherein in each circulation, the position and damping parameters of the damper and the rib plate layout of the three-dimensional box type structure are updated, and the optimization program is ended until an iteration termination condition is reached.
For the design model shown in fig. 3, the structural dimension is 1.6m × 1m × 0.3m, and the size of the simple harmonic load is F1:F2:F31:1:1, excitation frequency range is 0-300 Hz. Considering the symmetry of the box structure and the load, 2 dampers are arranged at symmetrical positions on the surface of the box structure, and the damping parameters of the dampers are the same. Maximum and minimum values T of rib plate thicknessmaxAnd Tmin15mm and 1mm respectively. The volume fraction η is set to 1.6, which means that 60% of the total volume of the initial box-type structure can be allocated to the reinforcing bars. The projection direction of the rib plate is a Z axis.
The layout of the rib plate of the three-dimensional box-type structure by adopting the self-adaptive growing method and the simultaneous optimization process of the rib plate and the damper are shown IN (a) to (e) of fig. 5, wherein a pentagram represents the position of the damper, and IN represents the iteration number. In the optimization step of the growth of each rib plate, the position of the damper can be changed along with the change of the layout of the rib plate, and meanwhile, the damping parameters can be updated. The final optimization results are shown in fig. 5 (d) to (e). The optimization iteration curve is as shown in fig. 6 (a), and the optimization process iterates 45 steps to converge. The dynamic compliance curve of the optimized box-type structure in the frequency domain is shown in fig. 6 (b).
In order to verify the superiority of the performance of the result of the simultaneous optimization method, the results of the simultaneous optimization method are compared with the results of the traditional non-simultaneous optimization method, namely, the layout of the rib plates of the box-type structure is optimized by adopting a self-adaptive growing method, and then the damper is arranged for tuning optimization. The dynamic performance of both pairs is shown in figure 7 and table 1,
TABLE 1 comparison of Performance parameters of the present invention with conventional non-simultaneous optimization methods
Figure BDA0002799869690000081
It can be seen that the maximum dynamic compliance amplitude of the simultaneous optimization result is significantly reduced compared with the amplitude of the result of the traditional non-simultaneous optimization method, and the performance is improved by about 58.2%. The comparative results demonstrate the superiority of the process of the invention.

Claims (1)

1. An optimization design method for anti-vibration structure dynamics comprises a design method for simultaneously optimizing the layout of rib plates of a three-dimensional engineering structure and an auxiliary damper, and adopts an optimization mathematical model as follows:
Figure FDA0003484856890000011
the design variables include: rib thickness T ═ T of engineering structure1,T2,…Tn]Stiffness k of the damperD＝[k1,k2,…,kN]And damping cD＝[c1,c2,…,cN]Position p of damper ═ p1,p2,…,pN]N and N are respectively the number of the rib plate units and the dampers, and the optimization aim is to minimize the dynamic flexibility of the engineering structure in the frequency domain
Figure FDA0003484856890000012
Calculated from the following formula:
Figure FDA0003484856890000013
wherein J (omega) is the dynamic flexibility of the engineering structure when the excitation frequency is omega0Is the upper limit of the excitation frequency range;
equation 1(c) is a modal balance equation of the engineering structure in a state where the damper is not installed, in order to determine the position of the damper; formula 1(d) represents the volume constraint of the engineered structure, v and v0Respectively representing the actual volume and the initial volume of the engineering structure, wherein eta is a volume fraction; equations 1(e) - (h) are upper and lower limit constraints for design variables, kminAnd kmaxRespectively the minimum value and the maximum value of the rigidity of the damper; c. CminAnd cmaxThe minimum value and the maximum value of the damping are respectively; in formula 1(h), N0Represents the maximum number of nodes of the engineering structure in the finite element model, which means the position p of the damperjCan be positioned on any node of the engineering structure in the finite element model;
the method comprises the following design steps:
1) initializing a design model, and defining optimization parameters;
2) carrying out modal analysis on the engineering structure without the damper;
3) optimal tuning of the damper, namely determining the optimal position and damping parameters of the damper: setting a target mode, namely the maximum mode displacement position of a mode needing vibration reduction as the position of the damper arrangement, then arranging the damper at the position, and optimizing the damping parameters of the damper by adopting an SQP sequence quadratic programming algorithm, wherein an optimized mathematical model is as follows:
Figure FDA0003484856890000021
in the formula, JmaxIs the maximum dynamic compliance, k, of the engineering structure in the target modejAnd cjIs the stiffness and damping of the jth damper, their initial values are calculated by the following equations:
Figure FDA0003484856890000022
wherein m is0Being the mass of the damper, ωMFor the natural frequency of the engineered structure in the target mode, μ is the mass ratio of the damper to the engineered structure, determined by:
Figure FDA0003484856890000023
wherein omega0Is the natural frequency of the damper0The modal mass for an engineered structure is calculated by:
Figure FDA0003484856890000024
wherein ω'MIs to add a mass m at the maximum modal displacement0After the mass block, the engineering structure has the natural frequency of a target mode;
by the method, the optimal tuning parameters of the damper can be obtained, and when the convergence condition is met, the optimization program exits and the optimal tuning process of the damper is finished;
4) harmonic response analysis and design sensitivity analysis of the damper-containing structure: establishing a finite element model of an engineering structure-damper system, obtaining the dynamic flexibility of the engineering structure in a frequency domain through harmonic response analysis, regarding the dynamic flexibility as an optimization target, and then carrying out design variable: thickness T of rib platehThe following formula is adopted for the analytical calculation of the sensitivity of (1):
Figure FDA0003484856890000031
wherein
Figure FDA0003484856890000032
And
Figure FDA0003484856890000033
a stiffness matrix and a mass matrix, u, divided into engineering structural unitseA displacement matrix that is a cell;
5) optimizing the layout of the rib plates by adopting a self-adaptive growing method to obtain a new engineering structure model; the self-adaptive growth method is based on the growth rule of a natural branch system, and for a box-type structure reinforcing rib structure, the rib plate can grow, diverge and degenerate according to a certain criterion from a seed line to finally obtain the optimal rib plate layout form;
and 2) repeatedly optimizing and circulating, wherein in each circulation, the position and the damping parameters of the damper and the rib plate layout of the engineering structure are updated until an iteration termination condition is reached, and the optimization program is ended.
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Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1524613A1 (en) * 2003-10-15 2005-04-20 Rieter Technologies A.G. Optimising method for vibration damping
CN108595789A (en) * 2018-04-04 2018-09-28 上海理工大学 A kind of constrained damping structure vibration radiation acoustical power hierarchy optimization design method

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CN110909496B (en) * 2019-11-06 2023-07-07 上海理工大学 Two-stage collaborative optimization design method for constraint damping structure
CN111859741B (en) * 2020-07-08 2022-09-20 大连理工大学 Reinforced slab shell structure damping layer topology and reinforced rib layout collaborative optimization method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1524613A1 (en) * 2003-10-15 2005-04-20 Rieter Technologies A.G. Optimising method for vibration damping
CN108595789A (en) * 2018-04-04 2018-09-28 上海理工大学 A kind of constrained damping structure vibration radiation acoustical power hierarchy optimization design method

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