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对四组带平面内边界条件的简支梯度柱形壳进行自由振动分析。假设其材料特性随壳厚度方向逐渐变化的温度而变化。通过指定柱外表面的高温以及内表面的温度来研究温度升高的作用,壳厚度方向的温度分布是通过在该方向的定态热传导来实现的。根据Love壳理论和Von Karman Donnell-type运动学非线性特性确定运动方程。首先采用静力分析确定热荷载作用下产生的预应力状态,静力分析采用控制方程以及Galerkin法推导的运动等式进行分析。结果指出了幂律指数对热环境下壳体的自振频率及模态的影响作用。
Free vibration analysis of four kinds of simply supported gradient cylindrical shells with in-plane boundary conditions. The material properties are assumed to vary with the temperature at which the shell thickness gradually changes. The effect of temperature increase is studied by specifying the high temperature at the outer surface of the column and the temperature at the inner surface. The temperature distribution in the direction of the shell thickness is achieved through the steady state heat conduction in this direction. The equation of motion is determined according to Love Shell theory and Von Karman Donnell-type kinematic nonlinearity. First of all, static analysis is used to determine the prestressing state under the action of thermal load. The static analysis is based on the governing equations and the equations of motion deduced by the Galerkin method. The results show that the influence of power law index on natural frequency and mode of shell under thermal environment.