基于高斯小波函数和线性表达法的开口板自由振动特性研究

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摘要研究开口板自振特性的求解方法，将开口部位视为厚度为零的板，引入局域化特性的高斯小波函数作为位移形函数来捕捉厚度突变的情况，提高解的精确度。本文提出线性表达方法解耦位移形函数与边界条件，基本思路是通过高斯消元法找到约束条件矩阵中线性无关的列向量，将位移形函数中的未知系数转变为线性无关系数列向量的线性表达，从而将有约束问题转变为无约束问题。对四边简支和四边固定的开口板进行分析，结合有限元方法计算结果，讨论解的收敛性和准确性。研究了不同开口尺寸、开口形状对自振频率的影响，得到开口尺寸、开口形状与自振频率关系曲线，对影响的原因进行了解释。最后计算了不同边界约束条件下多开口板的自振频率。

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	郭文杰
	柴天建
	颜建伟
	洪显

关键词 ：高斯小波函数, 线性表达法, 自振特性, 能量法, 开口板

Abstract：Research the solution method for the natural vibration characteristics of open plates, treating the open area as a plate with zero thickness, and introducing localized Gaussian wavelet functions as displacement shape functions to capture sudden changes in thickness, thereby improving the accuracy of the solution. In this paper, a linear expression method is proposed to decouple the displacement shape function and boundary conditions. The basic idea is to find the Linear independence column vector in the constraint matrix through the Gauss elimination method, and transform the unknown coefficient in the displacement shape function into the linear expression of the linearly independent sequence vector, thus transforming the constrained problem into the unconstrained problem. Analyze the simply supported and fixed open plates on four sides, and discuss the convergence and accuracy of the solution based on the finite element method calculation results. We have studied the influence of different opening sizes and shapes on natural frequency, obtained the relationship curve between opening size and shape and natural frequency, and explained the reasons for the influence. Finally, the natural frequencies of multi opening plates under different boundary constraints are calculated.

Key words： gaussian wavelet function linear expression method natural vibration characteristics energy method opening plate

收稿日期: 2023-06-13 出版日期: 2024-03-28

引用本文:

郭文杰，柴天建，颜建伟，洪显. 基于高斯小波函数和线性表达法的开口板自由振动特性研究[J]. 振动与冲击, 2024, 43(6): 29-37.
GUO Wenjie，CHAI Tianjian，YAN Jianwei，HONG Xian. Natural vibration characteristics of an open plate based on the Gaussian wavelet function and linear expression. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(6): 29-37.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2024/V43/I6/29

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