基于分析与设计序列迭代方法的三维声子晶体拓扑优化及参数分析

PDF(1428 KB)

振动与冲击 ›› 2025, Vol. 44 ›› Issue (4) : 97-104.

振动理论与交叉研究

基于分析与设计序列迭代方法的三维声子晶体拓扑优化及参数分析

王燕*1,2 ，朱奕筱 3，亢战 3

作者信息 +

Three-dimensional phononic crystals topology optimization via successive iteration of analysis and design, and parameter exploration

WANG Yan*1,2，ZHU Yixiao3，WU Shengchuan1，KANG Zhan3

Author information +

文章历史 +

摘要

在常规的声子晶体拓扑优化中，内层的多波矢特征值分析和外层的单胞布局设计变量寻优构成双层嵌套问题，两个层次嵌套式迭代求解导致三维拓扑优化设计面临计算量剧增的难题。本文为提高优化设计的效率，将用于结构固有频率优化问题的分析与设计序列迭代的思想拓展至三维声波声子晶体的拓扑优化，通过将内层特征值问题转化为单次逆迭代获得拓扑优化中间结果对应的逐次近似能带结构，并根据优化结果进行参数化建模以研究三维声子晶体拓扑优化解的带隙特性。通过参数化扫掠，给出了不同参数下的相对带隙和带隙上下界。论文进一步总结了不同参数对声子晶体带隙的影响，为三维声波声子晶体构型设计提供指导。

Abstract

Conventional topology optimization of PnCs needs to perform an inner eigenvalue analysis corresponding to many wave vectors, and an outer design optimization problem to find the optimal unit cell configuration. Such a double-loop nested problem becomes extremely computationally demanding for three-dimensional cases. In this study, based on the successive iteration of analysis and design method, topology optimization of three-dimensional acoustic PnCs is performed to improve the efficiency of design optimization. Therein, the inner loop problem is converted into a single-step inverse iteration to provide sequentially approximated band structures of the intermediate designs. According to the optimization results, several parametric models are built to study the bandgap properties of the optimized three-dimensional PnCs designs. The results of the relative bandgaps and their upper/lower bounds of the unit cells are given through parameter scanning. The influences of different parameters on the bandgap property are analyzed, which may provide useful guidance to the design of three-dimensional acoustic PnCs.

导出引用

王燕 1, 2, 朱奕筱 3, 亢战 3. 基于分析与设计序列迭代方法的三维声子晶体拓扑优化及参数分析[J]. 振动与冲击, 2025, 44(4): 97-104

WANG Yan1, 2, ZHU Yixiao3, WU Shengchuan1, KANG Zhan3. Three-dimensional phononic crystals topology optimization via successive iteration of analysis and design, and parameter exploration[J]. Journal of Vibration and Shock, 2025, 44(4): 97-104

参考文献

[1] Sigalas M M. Elastic and acoustic wave band structure [J]. Journal of sound and vibration, 1992, 158(2): 377-382.
[2] Kushwaha M S, Halevi P, Dobrzynski L, et al. Acoustic band structure of periodic elastic composites [J]. Physical review letters, 1993, 71(13): 2022-2025.
[3] 沈惠杰,李雁飞,苏永生,等.舰船管路系统声振控制技术评述与声子晶体减振降噪应用探索[J].振动与冲击,2017,36(15):163-170+209.
SHEN hui-jie, LI Yan-fei, SU Yong-sheng, et al. Ｒeview of sound and vibration control techniques for ship piping systems and exploration of photonic crystals applied in noise and vibration reduction [J]. Journal of Vibration and Shock, 2017, 36(15): 163-170+209.
[4] 温激鸿, 刘耀宗, 王刚, 等. 声子晶体弹性波带隙理论计算及实验研究[J]. 功能材料, 2004(05): 657-659.
WEN Ji-hong, LIU Yao-zong, WANG Gang, et al. Elastic wave band gaps of 1D and 2D phononic crystals: theory and experiment [J]. Journal of Functional Materials. 2004(05): 657-659.
[5] 李彬生,戴卓辰,张程,等.新型多共振腔声子晶体声屏障的带隙机理及其隔声性能研究[J].振动与冲击,2023,42(15):182-189+259.
LI Bin-sheng, DAI Zhuo-chen, ZHANG cheng, et al. Bandgap mechanism and sound insulation performance of a novel multi-resonant cavity sonic crystal sound barrier[J]. Journal of Vibration and Shock, 2023, 42(15): 182-189+259.
[6] 刘启能. 可调谐声子晶体滤波器的设计. 压电与声光[J], 2008(04): 408-410.
LIU Qi-neng. The Design of Tunable Photonic Crystal Filter [J]. Piezoelectrics & Acoustooptics, 2008(04): 408-410.
[7] 郝骞,杨鹏,韩建宁, 等. 声子晶体滤波特性研究[J]. 科学技术与工程[J], 2016, 16(06): 121-124.
HAO Qian, YANG Peng, HAN Jian-ning, et al. The Ｒesearch of Filtering Characteristics in Phononic Crystal [J]. Science Technology and Engineering, 2016, 16(06): 121-124.
[8] Wang Y F, Wang Y Z, Wu B, et al. Tunable and active phononic crystals and metamaterials [J]. Applied Mechanics Reviews, 2020, 72(4): 040801.
[9] Sainidou R, Stefanou N, Modinos A. Linear chain of weakly coupled defects in a three-dimensional phononic crystal: A model acoustic waveguide [J]. Physical Review B, 2006, 74(17): 172302.
[10] Ma T X, Li X S, Tang X L, et al. Three-dimensional acoustic circuits with coupled resonators in phononic crystals [J]. Journal of Sound and Vibration, 2022, 536: 117115.
[11] D'Alessandro L, Belloni E, Ardito R, et al. Modeling and experimental verification of an ultra-wide bandgap in 3D phononic crystal [J]. Applied Physics Letters, 2016, 109(22): 221907.
[12] Aravantinos-Zafiris N, Lucklum F, Sigalas M M. Complete phononic band gaps in the 3D Yablonovite structure with spheres [J]. Ultrasonics, 2021, 110: 106265.
[13] Lucklum F, Vellekoop M J. Realization of complex 3-D phononic crystals with wide complete acoustic band gaps [J]. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 2016, 63(5): 796-797.
[14] Lucklum F, Vellekoop M J. Design and fabrication challenges for millimeter-scale three-dimensional phononic crystals [J]. Crystals, 2017, 7(11): 348.
[15] Ma T X, Wang Y S, Zhang C. Photonic and phononic surface and edge modes in three-dimensional phoxonic crystals [J]. Physical Review B, 2018, 97(13): 134302.
16 Korozlu N, Kaya O A, Cicek A, et al. Acoustic Tamm states of three-dimensional solid-fluid phononic crystals [J]. The Journal of the Acoustical Society of America, 2018, 143(2): 756-764.
[17] Sigmund O, Søndergaard Jensen J. Systematic design of phononic band–gap materials and structures by topology optimization [J]. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2003, 361(1806): 1001-1019.
[18] Rupp C J, Evgrafov A, Maute K, et al. Design of phononic materials/structures for surface wave devices using topology optimization [J]. Structural and Multidisciplinary Optimization, 2007, 34: 111-121.
[19] Hussein M I, Hamza K, Hulbert G M, et al. Optimal synthesis of 2D phononic crystals for broadband frequency isolation [J]. Waves in Random and Complex Media, 2007, 17(4): 491-510.
[20] Dong H W, Su X X, Wang Y S, et al. Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm [J]. Structural and Multidisciplinary Optimization, 2014, 50: 593-604.
[21] Huang Y, Liu S T, Zhao J. Optimal design of two-dimensional bandgap materials for unidirectional wave propagation [J]. Structural and Multidisciplinary Optimization, 2013, 48: 487-499.
[22] Park J H, Ma P S, Kim Y Y. Design of phononic crystals for self-collimation of elastic waves using topology optimization method [J]. Structural and Multidisciplinary Optimization, 2015, 51: 1199-1209.
[23] 曹蕾蕾,武建华,樊浩, 等. 考虑可制造性约束的声子晶体多目标拓扑优化[J]. 力学学报, 2022, 54(04): 1136-1144.
CAO Lei-lei, WU Jian-hua, FAN hao, et al. Multi-objective topology optimization of phononic crystals considering manufacturing constraint [J]. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(04): 1136-1144.
[24] 邱克鹏,陈智谋,张建刚, 等. 基于形状记忆合金声子晶体的带隙优化设计[J]. 力学学报, 2023, 55(06): 1278-1287.
QIU Ke-peng, CHEN Zhi-mou, ZHANG Jian-gang, et al. Bandgap optimization design of phononic crystals based shape memory alloy [J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(06): 1278-1287.
[25] Lu Y, Yang Y, Guest J K, et al. 3-D phononic crystals with ultra-wide band gaps [J]. Scientific reports, 2017, 7(1): 43407.
[26] Li W B, Meng F, Li Y F, et al. Topological design of 3D phononic crystals for ultra-wide omnidirectional bandgaps [J]. Structural and Multi-disciplinary Optimization, 2019, 60: 2405-2415.
[27] Gao H, Qu Y H, Meng G. Topology Optimization and Wave Propagation of Three-Dimensional Phononic Crystals [J]. Journal of Vibration and Acoustics, 2023, 145(1): 011002.
[28] Van den Boom S J, Abedi R, van Keulen F, et al. A level set-based interface-enriched topology optimization for the design of phononic crystals with smooth boundaries [J]. Computer Methods in Applied Mechanics and Engineering, 2023, 408: 115888.
[29] Zhu Y X, Kang Z. A topology optimization framework for 3D Phononic Crystals via the method of successive iteration of analysis and design [J]. Composite Structures, 2023: 117641.
[30] Zhang X P, He J J, Takezawa A, et al. Robust topology optimization of phononic crystals with random field uncertainty [J]. International Journal for Numerical Methods in Engineering, 2018, 115(9): 1154-1173.