基于改进高斯展开法的ABH板弯曲振动特性分析

李剑辉1,郑玲1,邓杰2,李美玉1

振动与冲击 ›› 2023, Vol. 42 ›› Issue (8) : 87-95.

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PDF(2489 KB)
振动与冲击 ›› 2023, Vol. 42 ›› Issue (8) : 87-95.
论文

基于改进高斯展开法的ABH板弯曲振动特性分析

  • 李剑辉1,郑玲1,邓杰2,李美玉1
作者信息 +

Flexural vibration analysis of ABH plates based on an improved Gaussian expansion method

  • LI Jianhui1,ZHENG Ling1,DENG Jie2,LI Meiyu1
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文章历史 +

摘要

针对声学黑洞(Acoustic Black Hole,ABH)板存在的非均匀波长分布和波数快速变化问题,本文建立了一种基于改进高斯展开法(Improved Gaussian Expansion Method,IGEM)的半解析模型来分析ABH板的弯曲振动问题。在Rayleigh-Ritz法的框架下,选择高斯函数作为基函数,根据板的厚度变化来确定不同位置高斯基函数的尺度因子,并根据尺度因子和板的形状来确定高斯基函数的分布情况;通过尺度因子的分级化处理,既可以更加准确地描述板在不同厚度处的位移,又实现了 x 方向和 y 方向在积分过程中的分离,进而改善了计算准确度和效率;此外,根据板的形状确定高斯基函数的分布情况,可以避免质量矩阵和刚度矩阵的奇异化。本文以矩形ABH板、圆形ABH板和开孔形ABH板为例,验证了该方法在计算ABH板弯曲振动时的准确性和适用性。

Abstract

In view of non-uniform wavelength distribution and variable wave-number in Acoustic Black Hole (ABH) plates, a semi-analytical model based on the Improved Gaussian Expansion Method(IGEM) is proposed to analyze the flexural vibration of ABH plates. In the framework of the Rayleigh-Ritz method, Gaussian functions are used as basic functions to describe the displacement field around ABH plates. The scale factor of Gaussian functions is adjusted according to the variable thickness of the plate. Meanwhile, the distribution of Gaussian functions will be a function of the scale factor and the shape of the ABH plate. In this process, the scale factor is not a constant anymore as in traditional Gaussian Expansion method. Therefore, the displacement of the plate with different thicknesses can be described more accurately, and the separation of x direction and y direction in the integration process can be realized to improve the efficiency and accuracy in computation. The singularity of the mass and stiffness matrix can be avoided when Improved Gaussian Expansion Method is applied to ABH plates In this paper, a rectangular plate with ABH indentations, a circular plate with ABH indentations and a perforated plate with ABH indentations are taken account as examples. The results are compared with Finite Element method (FEM). Results show that the proposed method demonstrates  more accurate and less computation cost than the conventional Gaussian Expansion Method. This implies a potential application to predict the response characteristics of structures with thickness variation rapidly as ABH plates. 

关键词

半解析 / 高斯展开法 / Rayleigh-Ritz法 / 声学黑洞

Key words

semi-analytical / Gaussian expansion method / Rayleigh-Ritz method / Acoustic black hole (ABH)

引用本文

导出引用
李剑辉1,郑玲1,邓杰2,李美玉1. 基于改进高斯展开法的ABH板弯曲振动特性分析[J]. 振动与冲击, 2023, 42(8): 87-95
LI Jianhui1,ZHENG Ling1,DENG Jie2,LI Meiyu1. Flexural vibration analysis of ABH plates based on an improved Gaussian expansion method[J]. Journal of Vibration and Shock, 2023, 42(8): 87-95

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