热弹耦合圆板非线性振动的研究

对温度场中圆板的非线笥热弹耦合自由振动问题，由非线性振动方程、协调方程及热传导方程出发，动用伽辽金法求解，得出一个关于时间的非线笥常策分方程组。将热弹耦合与非热弹耦合情况进行对比，发现给定初始位移较小时，热弹耦合效应使板的固有频率相对与无热弹耦合情形提高；给定初始位移较大时，热弹耦合２使固有频率降低，该文不还比较了不同热弹参数和边界条件对热弹耦合效应的影响。

THE STUDY OF NON-LINEAR THERMOELASTIC VIBRATIONOF CIRCULAR PLATE

The problem of the free vibration of circular plate when temperature field and stress field are coupled is analyzed. From the nonlinear thermoelastic vibration equation, the compatibility equation and the conductive heat transfer equation, a system of nonlinear differential equation about time is obtained by Galerkin's method. The numerical result of vibration amplitude Vs time is compared with the case that the two fields are not coupled. It is found that when the given initial displacement is smaller, the natural frequency of circular plate in coupled case will be larger than the uncoupled case, and when the given initial displacement is larger, the natural frequency of circular plate in coupled case will be smaller than the uncoupled case. Some effect of different coefficients and boundary conditions on vibration are also discussed.