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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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

Received: 13 June 2023 Published: 28 March 2024

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	GUO Wenjie
	CHAI Tianjian
	YAN Jianwei
	HONG Xian

Cite this article:

GUO Wenjie,CHAI Tianjian,YAN Jianwei, et al. Natural vibration characteristics of an open plate based on the Gaussian wavelet function and linear expression[J]. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(6): 29-37.

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http://jvs.sjtu.edu.cn/EN/ OR http://jvs.sjtu.edu.cn/EN/Y2024/V43/I6/29

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