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对温度场中圆板的非线性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，运用伽辽金法求解，得出一个关于时间的非线性常微分方程组．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，热弹耦合效应使固有频率降低．该文还比较了不同热弹耦合参数和边界条件对热弹耦合效应的影响．
Based on the nonlinear vibration equation, the coordination equation and the heat conduction equation, the Galerkin method is used to solve the problem of nonlinear thermo-elastic coupling free vibration of the circular plate in temperature field. A nonlinear ordinary differential equation group about time is obtained. The comparison between thermo-elastic coupling and non-thermo-elastic coupling shows that when the initial displacement is small, the thermo-elastic coupling effect increases the natural frequency of the plate relative to the case without thermo-elastic coupling. When the initial displacement is large, the thermonoelastic coupling The effect reduces the natural frequency. The paper also compares the effects of different thermo-elastic coupling parameters and boundary conditions on thermo-elastic coupling effects.