高模态密度结构宽频振动分析的小波有限元方法实现

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

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 method,TFEM)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 method,WFEM)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。

Broadband vibration analysis of high modal density structures is one of key issues in acoustic vibration analysis field.The numerical analysis method realizing broadband vibration prediction is an important study content in this field.An effective broadband vibration numerical analysis method can provide accurate numerical solutions from low frequency domain to high frequency domain.However,due to obvious dissipation error and high calculation cost,it is difficult for traditional finite element method(TFEM)to provide accurate numerical solutions in high-frequency domain when performing broadband vibration analysis of high modal density structures,so using TFEM is impossible to realize effective broadband vibration analysis.While wavelet finite element method(WFEM)have potential advantages of solving efficiency in structural analysis and can greatly reduce effects of dissipation error.Here,firstly,a self-coupling algorithm for wideband vibration analysis based on WFEM theory was constructed,and then the framework of WFEM was introduced for wideband vibration analysis of high modal density structures to form a wideband wavelet finite element method(WWFEM).Furthermore,wide-band vibration analysis of high modal density thin plate structure having analytical solution was performed based on WWFEM numerical analysis method.Finally,vibration responses of this high modal density structure in wide frequency domain were predicted with test analysis method.Through contrastive analysis,the convergence of WFEM in high-frequency vibration analysis and its effectiveness for broadband vibration analysis were verified.It was shown that WFEM can provide a theoretical reference for solving broadband vibration analysis problems of cylindrical shells,curved shells and other high modal density structures.