Nonlinear eigenvalue analysis of thermoviscous acoustic problems using an equivalent source method

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2025-02-21 DOI:10.1016/j.enganabound.2025.106162

Meng-Hui Liang, Chang-Jun Zheng, Yong-Bin Zhang, Liang Xu, Shuai Wang, Chuan-Xing Bi

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Abstract

In this study, a nonlinear eigenvalue solver for the numerical solution of thermoviscous acoustic problems based on the equivalent source method (ESM) is developed. By using the idea of the ESM, the solutions to the thermoviscous formulations are coupled on the surface of the structure through the isothermal and non-slip conditions. The frequency-dependent nature of the transfer matrix in the system equation of ESM gives rise to a nonlinear eigenvalue problem (NLEP), presenting an additional challenge in the eigenvalue analysis. To tackle this issue, the contour integral method is employed to convert the NLEP into a generalized eigenvalue problem (GEVP). This contour integral method is effective for accurately identifying complex acoustic eigenvalues, which are frequently encountered in the context of thermoviscous acoustic problems. Numerical examples are provided to validate the effectiveness and accuracy of the proposed method, while simulations involving acoustic black hole and acoustic-structural interaction demonstrate its potential applicability in engineering applications.

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热粘性声学问题非线性特征值分析的等效源方法

本文提出了一种基于等效源法（ESM）的热粘性声学问题数值解的非线性特征值求解器。利用ESM的思想，通过等温和防滑条件将热粘性公式的解耦合到结构表面。ESM系统方程中传递矩阵的频率依赖性质导致了非线性特征值问题（NLEP），给特征值分析带来了额外的挑战。为了解决这一问题，采用轮廓积分法将NLEP问题转化为广义特征值问题（GEVP）。这种轮廓积分方法可以有效地准确识别热粘性声学问题中经常遇到的复杂声学特征值。通过数值算例验证了该方法的有效性和准确性，并对声黑洞和声-结构相互作用进行了仿真，验证了该方法在工程应用中的潜在适用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Engineering Analysis with Boundary Elements 工程技术-工程：综合

CiteScore

5.50

自引率

18.20%

发文量

368

审稿时长

56 days

期刊介绍： This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.