基于非负声强的约束阻尼板拓扑优化研究

PDF(2220 KB)

振动与冲击 ›› 2021, Vol. 40 ›› Issue (11) : 33-41.

论文

基于非负声强的约束阻尼板拓扑优化研究

吴振云，赵文畅，陈海波

作者信息 +

Topology optimization of constrained damping plate based on non-negative sound intensity

WU Zhenyun, ZHAO Wenchang, CHEN Haibo

Author information +

文章历史 +

摘要

基于非负声强(non-negative intensity，NNI)对约束阻尼板声辐射问题作了分析及探讨,对约束阻尼板的阻尼材料的最优分布问题进行研究。使用非负声强识别结构表面对远场声辐射占据主要贡献地位的区域。使用固体各向同性材料惩罚(solid isotropic material with penalization, SIMP)方法进行密度插值，建立以阻尼材料相对密度为设计变量，以阻尼材料的体积占比作为约束，以声辐射贡献最小为目标函数的优化模型，采用移动渐近算法求解优化模型。以四边固支板为例，分析平板振动表面对远场贡献显著的区域，对阻尼材料的分布进行了优化设计。算例结果验证了基于非负声强的拓扑优化算法在降噪优化设计中的有效性，同时具备改变结构振动辐射模式的潜力。

Abstract

Here, the acoustic radiation problem of constrained damping plate was analyzed and discussed based on the concept of non-negative intensity (NNI).The optimal distribution of damping material of constrained damping plate was studied.NNSI was applied to recognize the structure surface area with the main contribution to far-field sound radiation.Based on the solid isotropic material with penalization (SIMP) density interpolation scheme, an optimization model was established by taking the relative density of damping material as the design variable, the volume ratio of damping material as the constraint, and the surface area with the minimum contribution to sound radiation as the objective function.The moving asymptotic algorithm was used to solve the optimization model.Taking the plate with four fixed edges as an example, the vibration plate surface region with significant contribution to far-field was analyzed, and the distribution of damping material was designed optimally.The example results showed that the topology optimization algorithm based on NNI is effective in denoising optimization design, and has the potential to change the structural vibration radiation mode.

导出引用

吴振云，赵文畅，陈海波. 基于非负声强的约束阻尼板拓扑优化研究[J]. 振动与冲击, 2021, 40(11): 33-41

WU Zhenyun, ZHAO Wenchang, CHEN Haibo. Topology optimization of constrained damping plate based on non-negative sound intensity[J]. Journal of Vibration and Shock, 2021, 40(11): 33-41

参考文献

［1］WILLIAMS E G.Fourier acoustics: sound radiation and nearfield acoustical holography［M］.New York: Academic Press, 1999.
［2］WILLIAMS E G.Supersonic acoustic intensity［J］.Journal of the Acoustical Society of America, 1995, 97(1): 121-127.
［3］WILLIAMS E G.Supersonic acoustic intensity on planar sources［J］.Journal of the Acoustical Society of America, 1998, 104(5): 2845-2850.
［4］MAGALHAES M, TENENBAUM R A.Supersonic acoustic intensity for arbitrarily shaped sources［J］.Acta Acustica United With Acustica, 2006, 92(2): 189-201.
［5］MARBURG S, LOSCHE E, PETERS H, et al.Surface contributions to radiated sound power［J］.Journal of the Acoustical Society of America, 2013, 133(6): 3700-3705.
［6］WILLIAMS E G.Convolution formulations for non-negative intensity［J］.The Journal of the Acoustical Society of America, 2013, 134(2):1055-1066.
［7］WILKES D R, PETERS H, CROAKER P, et al.Non-negative intensity for coupled fluid-structure interaction problems using the fast multipole method［J］.Journal of the Acoustical Society of America, 2017, 141(6): 4278-4288.
［8］刘正浩，郑毅，黎胜.基于表面贡献法的船壳远场声辐射热区识别［J］.舰船科学技术,2017,39(7):34-38.
LIU Zhenghao, ZHENG Yi, LI Sheng.Identification of hull’s radiation hotspot to far-field based on the surface contribution method［J］.Ship Science and Technology, 2017, 39(7):34-38.
［9］DU J B, OLHOFF N.Minimization of sound radiation from vibrating bi-material structures using topology optimization［J］.Structural and Multidisciplinary Optimization, 2007, 33(4): 305-321.
［10］贺红林, 陶结, 袁维东, 等.约束阻尼板的渐进法结构减振拓扑动力学优化［J］.噪声与振动控制, 2016, 36(1):21-26.
HE Honglin, TAO Jie, YUAN Weidong, et al.Topological dynamic optimization for structure vibration reduction of constraint damping plates using evolutionary method［J］.Noise and Vibration Control, 2016, 36(1):21-26.
［11］ZHENG L, XIE R L, WANG Y, et al.Topology optimization of constrained layer damping on plates using method of moving asymptote (MMA) approach［J］.Shock and Vibration, 2011,18(1/2): 221-244.
［12］郑玲，谢熔炉，王宜，等.基于优化准则的约束阻尼材料优化配置［J］.振动与冲击, 2010, 29(11): 156-159.
ZHENG Ling, XIE Ronglu, WANG Yi, et al.Optimal placement of constrained damping material in structures based on optimality criteria［J］.Jourmal of Vibration and Shock, 2010, 29(11): 156-159.
［13］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 Qiaofei.Topology optimization for the acoustic radiation of constraint damping plate［J］.Jourmal of Vibration and Shock, 2014, 33(5): 91-96.
［14］李鸿秋,陈国平,张保强.考虑声振耦合下结构阻尼板降噪拓扑优化设计［J］.振动、测试与诊断,2011,31(5):586-590.
LI Hongqiu, CHEN Guoping, ZHANG Baoqiang.Topology optimization design of constrained layer damping plate-cavity system considering vibro-acoustic coupling［J］.Journal of Vibration, Measurement & Diagnosis, 2011,31(5):586-590.
［15］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 Yinong, 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.
［16］窦松然, 桂洪斌, 李承豪, 等.圆柱壳振动控制中约束阻尼拓扑优化研究［J］.振动与冲击, 2015, 34(22):154-158.
DOU Songran, GUI Hongbin, LI Chenghao, et al.Topological optimization for constrained damping in vibration control of cylindrical shell［J］.Journal of Vibration and Shock, 2015, 34(22):154-158.
［17］王明旭,陈国平.基于变密度方法约束阻尼层动力学性能优化［J］.南京航空航天大学学报,2010,42(3):283-287.
WANG Mingxu, CHEN Guoping.Dynamics performance optimization of constrained damping layer using variable density method［J］.Journal of Nanjing University of Aeronautics & Astronautics, 2010, 42(3):283-287.
［18］BENDSE M P, SIGMUND O.Material interpolation schemes in topology optimization［J］.Archive of Applied Mechanics, 1999,69(9): 635-654.
［19］杜建镔，宋先凯，董立立.基于拓扑优化的声学结构材料分布设计［J］.力学学报,2011,43(2):306-315.
DU Jianbin, SONG Xiankai, DONG Lili.Design of material distribution of acoustic structure using topology optimization［J］.Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(2): 306-315.
［20］KANG Z, ZHANG X P, JIANG S G, et al.On topology optimization of damping layer in shell structures under harmonic excitations［J］.Structural and Multidisciplinary Optimization, 2012, 46(1): 51-67.
［21］李攀,郑玲,房占鹏.SIMP插值的约束层阻尼结构拓扑优化［J］.机械科学与技术,2014,33(8):1122-1126.
LI Pan, ZHENG Ling, FANG Zhanpeng.Topology optimization of constrained layer damping structure based on SIMP interpolation method［J］.Mechanical Science and Technology for Aerospace Engineering, 2014,33(8):1122-1126.
［22］许智生, 黄其柏, 赵志高, 等.基于拓扑优化方法的安静结构设计［J］.华中科技大学学报(自然科学版), 2010,38(4):91-94.
XU Zhisheng, HUANG Qibai, ZHAO Zhigao, et al.Quiet structure design based on topology optimization［J］.Journal of Huazhong University of Science and Technology (Natural Science Edition)， 2010,38(4):91-94.
［23］SVANBERG K.The method of moving asymptotes: a new method for structural optimization［J］.International Journal for Numerical Methods in Engineering, 1987, 24(2): 359-373.
［24］PETERS H, KESSISSOGLOU N, MARBURG S, et al.Enforcing peciprocity in numerical analysis of acoustic radiation modes and sound power evaluation［J］.Journal of Computational Acoustics, 2012, 20(3):1250005.
［25］YUN K S, YOUN S K.Topology optimization of viscoelastic damping layers for attenuating transient response of shell structures［J］.Finite Elements in Analysis and Design, 2018,141: 154-165.
［26］ZHAO W C, ZHENG C J, LIU C, et al.Minimization of sound radiation in fully coupled structural-acoustic systems using FEM-BEM based topology optimization［J］.Structural and Multidisciplinary Optimization, 2018, 58(1): 115-128.
［27］ZHAO W C, CHEN L L, CHEN H B, et al.Topology optimization of exterior acoustic-structure interaction systems using the coupled FEM-BEM method［J］.International Journal for Numerical Methods in Engineering, 2019, 119(5): 404-431.
［28］XU S L, CAI Y W, CHENG G D, et al.Volume preserving nonlinear density filter based on heaviside functions［J］.Structural and Multidisciplinary Optimization, 2010, 41(4): 495-505.