非平稳激励下薄板结构减振附加阻尼层的拓扑优化

摘要
图/表
参考文献(36)
相关文章 (15)

全文: PDF (1015 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要讨论了附加阻尼层的薄板结构在非平稳随机力作用下以减振为目标的阻尼材料层的拓扑优化问题。建立了以阻尼材料的相对密度为设计变量，以结构非平稳响应位移方差最小化为目标和阻尼材料用量为约束条件的拓扑优化模型。由于结构受到非平稳随机激励作用，其随机响应可以采用时域显式法快速求解；随机响应方差对设计变量的灵敏度采用了基于伴随变量法的时域显式法进行分析，并采用优化准则法求解优化问题。数值算例验证了所提方法在非平稳随机激励作用下进行动力拓扑优化减振的可行性与有效性。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	李雪平
	林猛峰
	魏鹏
	苏成

关键词 ：非平稳随机激励, 薄板结构, 附加阻尼层, 减振, 拓扑优化

Abstract：This paper investigates the optimal distribution of damping material on thin-plate structures under non-stationary stochastic excitation.In the topology optimization model, the relative densities of the damping material were taken as design variables, and the design objective is to minimize the structural displacement variances at specified positions under a given volume constraint of damping material.Since the structure was subjected to non-stationary stochastic force, the stochastic responses were solved rapidly based on an explicit time domain method (ETDM).The analysis of the displacement variance sensitivity was implemented by using the ETDM based on an adjoint variable method.Then the topology optimization problem was solved with an optimal criteria (OC) method.Numerical examples illustrate the feasibility and effectiveness of the proposed method for vibration attenuation of structures through dynamic topology optimization of damping layer under non-stationary stochastic excitation.

Key words： non-stationary stochastic excitations thin plate structures added damping layer vibration attenuation topology optimization

收稿日期: 2018-09-27 出版日期: 2020-04-15

引用本文:

李雪平，林猛峰，魏鹏，苏成. 非平稳激励下薄板结构减振附加阻尼层的拓扑优化[J]. 振动与冲击, 2020, 39(8): 250-257.
LI Xueping, LIN Mengfeng, WEI Peng, SU Cheng. Topology optimization of attached damping layers on thin plate structures for vibration attenuation under non-stationary stochastic excitations. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(8): 250-257.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I8/250

[1] Bendsøe M P, Kikuchi N. Generating optimal topologies in structural design using a homogenization method[J]. Computer Methods in Applied Mechanics and Engineering, 1988,71(2):197-224. [2] Bendsøe M P, Sigmund O. Material interpolation schemes in topology optimization[J]. Archive of Applied Mechanics, 1999, 69(9-10):635-654. [3] Rietz A. Sufficiency of a finite exponent in SIMP (power law) methods[J]. Structural Multidisciplinary Optimization, 2001, 21(2):159-163. [4] Xie Y M, Steven G P. A simple evolutionary procedure for structural optimization [J]. Computers and Structures, 1993, 49(5):885-896. [5] O.M. Querin, G.P. Steven, Y.M. Xie, Evolutionary structural optimisation (ESO) using a bidirectional algorithm, Eng. Comput. 15 (8) (1988) 1031-1048. [6] 杨德庆，刘正兴，隋允康.连续体结构拓扑优化设计的ICM方法[J]. 上海交通大学学报, 1999, 33(6):734-736. YANG De-qing, LIU Zheng-xing, SUI Yun-kang. ICM method for topology optimization design of continuum structures [J]. Journal of Shanghai Jiaotong University, 1999, 33(6):734-736. [7] Wang M Y, Wang X M, Guo D M, A level set method for structural topology optimization[J]. Computer Methods in Applied Mechanics and Engineering, 2003, 192(1):227-246. [8] Allaire G, Jouve F, Toader A M, Structural optimization using sensitivity analysis and a level-set method[J], J. Comput. Phys. 2004,194 (1):363-393. [9] 王睿, 张晓鹏, 亢战. 以动柔度为目标的结构阻尼材料层拓扑优化[J]. 振动与冲击, 2013, 32(22):36-40. Wang Rui, Zhang Xiao-peng, Kang Zhan. Topology optimization of damping layer in structures for minimizing dynamic compliance[J]. Journal of Vibration & Shock, 2013, 32(22):36-40. [10] 王睿, 张晓鹏, 吴良武,等. 考虑瞬态响应的薄板结构阻尼材料层拓扑优化[J]. 工程力学, 2015, 32(6):1-7. Wang Rui, Zhang Xiao-peng, WU Liang-wu, et al. Topology optimization of damping layer in thin-plate structures considering transient response[J]. Engineering Mechanics, 2015, 32(6):1-7,14. [11] 房占鹏,郑玲,唐重才,等.指定频带简谐激励下约束阻尼结构拓扑优化[J].振动与冲击,2015,(14):135-141. FANG Zhan-peng, ZHENG Ling, TANG Chong-cai. et al. Topology optimization for constrained layer damping structures under specified band harmonic excitations[J]. Journal of Vibration and Shock, 2015,(14):135-141. [12] Kang Z, Zhang X P, Jiang S G, et al. On topology optimization of damping layer in shell structures under harmonic excitations[J]. Structural & Multidisciplinary Optimization, 2012, 46(1):51-67. [13] 房占鹏, 侯俊剑, 姚雷. 简谐力激励下约束阻尼结构动力学拓扑优化[J]. 噪声与振动控制, 2018(s1). Fang Zhan-peng, Hou Jun-jian, Yao L. Dynamic Topology Optimization of Constrained Layer Damping Structure under Harmonic Force Excitation[J]. Noise & Vibration Control, 2018(s1). [14] Yan K, Cheng G D, Wang B P. Topology optimization of damping layers in shell structures subject to impact loads for minimum residual vibration[J]. Journal of Sound & Vibration, 2018, 431:226-247. [15] 杨德庆. 动响应约束下阻尼材料配置优化的拓扑敏度法[J]. 上海交通大学学报, 2003, 37(8):1209-1212. YANG De-qing. Topological sensitivity method for the optimal placement of unconstrained damping materials under dynamic response constraints[J].Journal of Shanghai Jiaotong University, 2003, 37(8):1209-1212. [16] 张桥,张卫红,朱继宏,等.动力响应约束下的结构拓扑优化设计[J].机械工程学报,2010,46(15):45-51. ZHANG Qiao, ZHANG Wei-hong, ZHU Ji-hong, et al. Topology optimization of structures under dynamic response constraints[J]. Journal of Mechanical Engineering, 2010,46(15):45-51. [17] 李超, 李以农, 施磊,等. 圆柱壳体阻尼材料布局拓扑优化研究[J]. 振动与冲击, 2012, 31(4):48-52. LI Chao, LI Yi-nong, SHI Lei, et al. Topological optimization for placement of damping material on cylindrical shells[J]. Journal of Vibration and Shock, 2012, 31(4):48-52. [18] Yun K S, Youn S K. Topology optimization of viscoelastic damping layers for attenuating transient response of shell structures[J]. Finite Elements in Analysis & Design, 2018, 141:154-165. [19] Zhang X, Kang Z. Topology optimization of damping layers for minimizing sound radiation of shell structures[J]. Journal of Sound & Vibration, 2013, 332(10):2500-2519. [20] 张志飞, 倪新帅, 徐中明,等. 基于优化准则法的自由阻尼材料拓扑优化[J]. 振动与冲击, 2013, 32(14):98-102. Zhang Zhi-fei, Ni Xin-shuai, Xu Zhong-ming, et al. Topologic optimization of a free damping material based on optimal criteria method[J]. Journal of Vibration & Shock, 2013, 32(14):98-102. [21] 徐伟, 张志飞, 庾鲁思,等. 附加自由阻尼板阻尼材料降噪拓扑优化[J]. 振动与冲击,2017, 36(11):192-198. Xu Wei, Zhang Zhi-fei, Yu Lu-si, et al. Topology optimization for noise reduction of structures with free damping[J]. Journal of Vibration & Shock, 2017, 36(11):192-198 and 223. [22] 郑玲, 祝乔飞. 约束阻尼板结构振动声辐射优化[J]. 振动与冲击, 2014, 33(5):91-96. ZHENG Ling, Zhu Qiao-fei. Topology optimization for acoustic radiation of a constraint damping plate[J]. Journal of Vibration & Shock, 2014, 33(5):91-96+108. [23] Rong J H, Tang Z L, Xie Y M, et al. Topological optimization design of structures under random excitations using SQP method[J]. Engineering Structures, 2013, 56(6):2098-2106. [24] Zhang W, Liu H, Gao T. Topology optimization of large-scale structures subjected to stationary random excitation[M]. Pergamon Press, Inc. 2015. [25] 苏成,徐瑞.非平稳随机激励下结构随机振动时域分析法[J].工程力学,2010,27(12):77-83. SU Cheng, XU Rui. Random vibration analysis of structures subjected to non-stationary excitations by time domain method[J]. Engineering Mechanics, 2010,27(12):77-83. [26] 苏成,徐瑞.非平稳随机激励下结构体系动力可靠度时域解法[J]. 力学学报,2010,42(3):512-520. SU Cheng, XU Rui. Time-domain method for dynamicreliability of structural systems subjected to non-stationaryrandom excitations[J]. Chinese Journal of Theoretical andApplied Mechanics, 2010, 42(3): 512-520. [27] Hu Z Q, Su C, Chen T C, et al. An explicit time-domain approach for sensitivity analysis of non-stationary random vibration problems[J]. Journal of Sound & Vibration, 2016, 382:122-139. [28] Hu Z Q, Wang Z Q, Su C, et al. Reliability Based Structural Topology Optimization Considering Non-stationary Stochastic Excitations[J]. Ksce Journal of Civil Engineering, 2018, 22(3):993-1001. [29] 李雪平, 李栋泓, 魏鹏,等. 非平稳随机地震响应约束下的桁架结构形状与拓扑优化[J]. 振动与冲击, 2017, 36(9):138-145. LI Xue-ping, LI Dong-hong, WEI Peng, et al. Shape and topology optimization of truss structures under non-stationary stochastic seismic excitations[J]. Journal of Vibration & Shock, 2017, 36(9):138-145. [30] Zheng L , Xie R L, W Yi, et al. Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach[J]. Shock & Vibration, 2011, 18(1-2):221-244. [31] Svanberg K. A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations[J]. Siam Journal on Optimization, 2009, 12(2):555-573. [32] Bendsoe, M P, Sifmund O. Topology optimization: theory, methods, and applications[M]. New York:Springer, 2003. [33] Newmark N M. A Method of Computation for Structural Dynamics[J]. Proc Asce, 1959, 85(1):67-94. [34] 余超. 基于时域显式法的结构瞬时最优控制[D]. 广州：华南理工大学, 2015. YU Chao. Instantaneous optimal control of seismically excited structures based on time domain explicit method[D]. Guangzhou: South China University of Technology, 2015.. [35] 房占鹏. 薄壁构件约束阻尼结构动力学拓扑优化研究[D]. 重庆大学, 2015. Fang Zhan-peng. Research on Dynamic Topology Optimization of Thin Wall Structure with Constrained Layer Damping Treatment[D]. Chongqing University , 2015. [36] Sigmund O. On the Design of Compliant Mechanisms Using Topology Optimization[J]. Journal of Structural Mechanics, 1997, 25(4):493-524.