变厚各向异性高速旋转圆盘在温度场作用下的振动问题摄动分析

Asymptotic Analysis of the Transverse Vibration of an Orthotropic High Speed Rotating Disk With Varying Thickness and Density in Thermal Field

本文研究了变厚度变密度各向异性高速自由旋转薄圆盘在温度场作用下的受力及振动特性。采用Frobenius法求出了圆盘面內位移及应力的级数解。通过摄动分析和加权积分,得到了圆盘横向振动固有频率的渐近解。文中还以纤维增强复合材料为例进行了实际计算。

In this paper an attempt has been made to investigate the stress and transverse vibra- tion characteristics of an orthotropic high speed rotating disk with varying thichness and density under thermal effect of steady heat conduction, The exact solutions in series form to the inward displacement and the stress of the disk have been given.The asymptotic solutions of vibration models and frequencies have been obtained by employing Frobenius method and weighted quadrature. A fiber reinforced composite material was used as an example to illustrate the vibration characteristics of the disk. It has been shown that the vibration frequency strongly depends on thermal distribution and orthotropic parameter β.