Abstract:

The effects of a cutout or hole inside a freely vibrating rectangular plate on the dynamics of an elastic plate are investigated. A general superellipse representation is employed to describe the boundary shape of the cutout, and a general FE analyzer ANSYS is used to evaluate the natural frequencies of the perforated plate. Numerical results show that the plate frequencies are highly dependent upon the shape, size, position and orientation of the cutout. Moreover, the effect is also highly related to the boundary conditions of the plate. In a practical engineering application, the design of a cutout within a thin rectangular plate deserves careful consideration so as to control the dynamic behaviors of the plate.

Key words: vibration and wave, cutout shape design, superellipse representation, rectangular plate, eigenfrequency

摘要：

以超椭圆方程描述开孔边界，利用ANSYS有限元软件，数值分析开孔的形状、面积（尺寸）、位置及转动对典型矩形板前二阶固有频率的影响。研究结果发现开孔能显著改变矩形板的固有频率，其影响效果受板的边界约束条件和开孔形状设计影响很大。实际工程结构中，开孔形状设计应当引起足够的重视。

关键词: 振动与波, 开孔形状, 超椭圆方程, 矩形板, 固有频率