高模态密度结构宽频振动分析的小波有限元方法实现

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (1) : 54-65.

论文

耿佳1,2,李明1,2,张兴武1,2,杨来浩1,2,陈雪峰1,2

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Implementation of WFEM for broadband vibration analysis of high modal density structures

GENG Jia1,2, LI Ming1,2, ZHANG Xingwu1,2, YANG Laihao1,2, CHEN Xuefeng1,2

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文章历史 +

摘要

高模态密度结构的宽频振动分析问题是声振分析领域内关注的重点问题之一，可实现宽频振动预测的数值分析方法是该领域内重要的研究内容，有效的宽频振动数值分析方法应在低频至高频域可同时提供精准的数值解。然而，由于明显的耗散误差和计算成本过高导致传统有限元方法（Traditional Finite Element Methods, TFEMs）在对高模态密度结构进行宽频振动分析时，难以在高频域提供精准的数值解，致使无法实现有效的宽频振动分析。而小波有限元分析方法（Wavelet Finite Element Methods, WFEMs）在进行结构分析时具有潜在的求解效率优势，并且可大幅度降低耗散误差带来的影响。为此，本文首先构造了基于小波有限元理论进行宽频振动分析时的自耦合算法，并据此介绍了小波有限元方法对高模态密度结构进行宽频振动分析的架构，形成了宽频小波有限元分析方法（Wide Wavelet Finite Element Method, WWFEM）。随后，采用数值分析研究方法，基于WWFEM对具有解析解的高模态密度薄板结构进行了宽频振动分析。最后，采用实验分析研究方法，预测了高模态密度结构在宽频域内的振动响应。在此基础上，对比分析了小波有限元方法在进行高频振动分析时的收敛性和宽频振动分析的有效性等。可为依据小波有限元分析方法解决圆柱壳、曲壳等高模态密度结构宽频振动分析问题提供理论参考。

Abstract

The dynamic analysis of high-modal density structures in a wide-frequency domain is a significant problem in the field of acoustic and dynamic analysis. As well known, the numerical methods should provide the accurate numerical solutions in both low and high frequency domains when proceeding the dynamic analysis in a wide-frequency domain. However, due to the obvious dispersion errors and high computational cost, Traditional Finite Element Methods (TFEMs) are difficult to provide accurate numerical solutions in the high-frequency domain when performing the dynamic analysis of high-modal-density structures. Fortunately, the Wavelet Finite Element Methods (WFEMs) have potential solution to provide the accurate numerical solutions with low computational cost when proceeding the structural analysis. Meanwhile, the WFEMs can greatly reduce the impact of dispersion errors when proceeding the dynamic analysis with refined mesh. Firstly, this paper will mainly introduce the formula to construct the self-coupling algorithm based on the WFEMs and discusses the detailed procedure of the wavelet finite element methods when performing the dynamic analysis of the high-modal density structures in a wide-frequency domain. In view of the above, a thin plate, which has analytical solutions, with high modal density is adopted for analyzing the numerical stability and validity of wavelet finite element in a wide-frequency domain when proceeding the dynamic analysis. Therefore, the convergence and validity of wavelet finite element method in high-frequency domain and wide-frequency domain is compared with the traditional finite element methods based on the numerical and experimental studies. It provides a theoretical reference for solving the problem of wide-frequency dynamic analysis of high-modal density structures, such as cylindrical and shells based on wavelet finite element methods.

导出引用

耿佳1,2,李明1,2,张兴武1,2,杨来浩1,2,陈雪峰1,2. 高模态密度结构宽频振动分析的小波有限元方法实现[J]. 振动与冲击, 2023, 42(1): 54-65

GENG Jia1,2, LI Ming1,2, ZHANG Xingwu1,2, YANG Laihao1,2, CHEN Xuefeng1,2. Implementation of WFEM for broadband vibration analysis of high modal density structures[J]. Journal of Vibration and Shock, 2023, 42(1): 54-65

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