基于双边Lanczos算法的声子晶体复模态重分析  

Complex modal reanalysis of phononic crystals based on two-sided Lanczos algorithm

作　　者：王亚茹 王刚[1,2,3] 安玉民 WANG Ya-ru;WANG Gang;AN Yu-min(College of Mechanical Engineering,Hebei University of Technology,Tianjin 300401,China;Tianjin Key Laboratory of Power Transmission and Safety Technology for New Energy Vehicles,Tianjin 300130,China;National Engineering Technology Research Center for Technology Innovation Methods and Tool,Tianjin 300401,China)

机构地区：[1]河北工业大学机械工程学院,天津300401 [2]天津市新能源汽车动力传动与安全技术重点实验室,天津300130 [3]国家技术创新方法与实施工具工程技术研究中心,天津300401

出　　处：《计算力学学报》2024年第2期299-305,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(12072099,11832011);河北省自然科学基金(A2021202023)资助项目.

摘　　要：针对声子晶体拓扑结构修改时模态计算效率低的问题,提出基于双边Lanczos算法的复模态重分析。与全分析不同,本方法利用声子晶体原始结构的模态分析结果,通过双边Lanczos算法构建投影向量矩阵,将广义特征值方程映射进子空间来压缩矩阵规模,求解方程后再利用近似模态关系得到最终解。通过对尺寸和形状发生修改的声子晶体进行分析,验证了方法所求结果具有高精度,与全分析相比缩减了约35%的计算时间,在处理拓扑修改变化量大和计算规模大的声子晶体模态分析问题上有很大潜力。Aiming at solving the problem of low efficiency in modal analysis when the topology of phononic crystals is modified,a complex modal reanalysis based on two-sided Lanczos algorithm was proposed.Different from the full analysis,the modal analysis results of the original structure of the phononic crystals are used in the presented method.The projection vector matrix is constructed by applying the two-sided Lanczos algorithm.The scale of the vector matrix is compressed by mapping the generalized eigenvalue equation into the subspace.After solving the equation,the final solution is obtained by using the approximate modal relation.Through the analysis of the phononic crystals with their size and shape modified,it is verified that the results obtained by the method are of high accuracy,and the calculation time is reduced by 35%compared with that of full analysis.The method has a great potential in dealing with the modal analysis problems of phononic crystals with large topological modification variation and large calculation scale.

关 键 词：双边Lanczos算法 复模态重分析 广义特征值问题 声子晶体 

分 类 号：U270[机械工程—车辆工程] O242.1[交通运输工程—载运工具运用工程]