变厚度圆板、环板振动分析的传递矩阵法*

变厚度圆板和环板是在工程设计中经常遇到的一类构件,与等厚度板相比,通过适当的沿径向厚度的变化,这种变厚度板在振动、失稳、弯曲等方面能起到更好的效果。将沿径向任意变厚度圆板、环板划分为一系列等厚度环板单元,基于Mindlin中厚板理论采用逆向推导的方式推导了其传递矩阵,建立起变厚度圆板、环板的频率方程。通过计算线性变厚度环板自由振动时的频率,并与ANSYS模态分析结果相比较,验证了计算模型的精确性。逆向推导法避免了高阶数传递矩阵推导复杂的问题,是对传递矩阵法的很好推广。

Transfer matrix method of vibration analysis for circular and annular plates with variable thickness

Plates with variable thickness are used widely in many engineering structures and machines. By appropriate variation of the plate thickness these tapered plates can have significantly greater efficiency for bending, bucking, and vibration as compared to plates of uniform thickness. The circle or annular plate with tapered thickness is divided into a series of annular plate with uniform thickness along its radial direction, and its transfer matrix is deduced using the backward-deduction method based on the Mindlin theory for moderate-thick plates. Then the frequency equation of the circle and annular plate with tapered thickness is formulated by applying principle of transfer matrix method. Numerical results are presented for completely free, annular plate with linear variation in thickness, and the accuracy of the calculation model is verified by comparisons made between results obtained from transfer matrix method and that obtained from ANSYS. The backward-deduction method avoids complex deduction of the higher order transfer matrix, which is a beneficial promotion of transfer matrix method.