大尺寸比结构声振耦合分析的自适应半解析计算模型研究

Structural-acoustic coupling analysis has extensive applications in a broad field of sciences and engineering, such as aerospace, ships, high-speed trains, industrial machinery and some other complex equipments. However, traditional numerical simulation of the acoustic-vibration coupling response of the large-size-ratio structures often encounters the computational challenges such as lower numerical accuracy in some localized regions and a rapid growth of computational complexity with increasing size ratio. Here the large-size-ratio structures refer to the slender structures, the structures consist of the size-disparity components and the composite material structures with the size-disparity matrix and inclusions and so on. This proposal is aimed at combining the adaptive node technique and the semi-analytical singular boundary method (SBM) jointly proposed by the applicant, and then applying the fast matrix solvers to efficiently accelerate the present SBM simulation for the exterior acoustic fields of the large-size-ratio structures. Moreover, we will develop the semi-analytical meshless collocation method (SAMCM) in conjunction with the extended precision arithmetic (EPA), and then introduce the parallel-acceleration domain decomposition method and the adaptive extended precision technique into EPA-based SAMCM for efficiently simulating the vibration response of large-size-ratio structures. Finally, the appropriate coupling strategy for SBM and EPA-based SAMCM is carefully developed to establish the related semi-analytical coupling model. In the proposed coupling model, we desire to reduce the discretization requirement per wavelength to 3-5 nodes for the structural-acoustic coupling analysis of the large-size-ratio structures. The purpose of this proposal is to establish a high performance computational model for the structural-acoustic coupling analysis of the large-size-ratio structures to meet the growing demands in the accuracy and efficiency of the computational model for the optimization design of the noise and vibration reduction of the complex equipments.

结构声振耦合分析在航空航天、船舶、高速列车及机械等复杂装备领域具有广泛应用。传统数值模型模拟细长结构、构件尺寸悬殊的组合结构、基体与夹杂尺寸悬殊的复合材料结构等大尺寸比结构的声振耦合响应时仍存在局部区域计算精度低、计算量随尺寸比增大而迅速增加等挑战性难题。本项目拟将申请者参与提出的半解析奇异边界法与节点自适应技术相结合，引入矩阵快速求解技术，用于高效模拟大尺寸比结构的外部声场；发展基于扩展精度技术的半解析无网格配点法，引入区域分解并行加速技术和扩展精度位数自适应技术，用于高效模拟大尺寸比结构振动响应；发展适用于奇异边界法和半解析无网格配点法的耦合策略，建立相应的半解析耦合计算模型，将数值模拟大尺寸比结构声振耦合响应时一个波长内所需的平均节点数控制在3-5个。目标是建立模拟大尺寸比结构声振耦合响应的高性能计算模型，以满足复杂装备减振降噪优化设计领域对计算模型在精度、效率等方面日益增长的需求。

结构声振耦合分析在航空航天、船舶、高速列车及机械等复杂装备领域具有广泛应用。传统数值模型模拟细长结构、构件尺寸悬殊的组合结构、基体与夹杂尺寸悬殊的复合材料结构等大尺寸比结构的声振耦合响应时仍存在局部区域计算精度低、计算量随尺寸比增大而迅速增加等挑战性难题。本项目发展了用于结构声振耦合分析的奇异边界法-有限元耦合计算模型，并引入递归骨架分解技术实现了上百万节点离散的三维大尺寸结构声振耦合分析。同时基于直接耦合策略，发展了奇异边界法-广义有限差分法耦合计算模型，并将其成功用于均质和复合材料结构的声振耦合响应分析。还将最新提出的局部半解析配点法与奇异边界法相结合，构建耦合计算模型用于结构声振耦合分析。此外，本项目还先后发展了功能梯度碳纳米管增强复合材料板模态分析的广义有限差分法，用于奇异边界法处理无限域声场中虚假特征频率问题的自正则CHIEF法，声子晶体波传播特性分析的局部半解析配点法、基于扩展精度技术的半解析配点法以及基于双层/多层节点迭代技术的快速声学奇异边界法。成果方面，团队成员基于上述研究内容申请获得6项软件著作权，并发表相关学术论文38篇（包括35篇SCI检索论文），获得国家自然科学基金优秀青年项目、德国洪堡学者奖学金、杜庆华工程计算方法优秀青年学者奖（ICCM2019）、国际计算方法青年学者奖和国际华人计算力学协会青年学者奖，2次入选爱思唯尔中国高被引学者名单。人才培养方面，依托项目培养博士研究生7名、硕士研究生8名，其中2名研究生已顺利获得博士学位、6名研究生已顺利获得硕士学位。本项目也极大地促进了项目组成员的学术交流，组织4次专题研讨会，参加国内外学术会议并做邀请报告6次，出国访学4人次、合作来访（含线上报告会）15人次。综上所述，项目在大尺寸比结构声振耦合分析的自适应半解析计算模型研究方面达到了预期目标，促进了科研团队的发展，培养了科研人才。