变厚度三角板和矩形板的自由振动

本文用Ritz方法分析了变厚度三角板和矩形板的自由振动。首先为求解任意三角板的自由振动构造了一种合适的振型函数。在理论和计算成果的分析基础上提出了计算变厚度矩形板自由振动频率参数的近似公式。最后分析了泊松比对薄板自由振动的影响。文中各种计算结果得到了实验结果或文献成果的验证。

The Free Vibration of Triangular and Rectangular Plates with Varying Thickness

In this paper, Ritz method is applied to the free vibration analysis of plates. A suitable shape function for triangular plates is selected. According to the theoretical analysis and calculative data, this paper presents an approximate formula for calculating the vibration frequency parameters of rectangular plates with linearly varying thickness. The effects of changing Poisson's ratio upon the vibration frequency parameters are studied. For all the calculating results obtained from this study are verified by those from experimental results and current literatures.