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在沿厚度方向线性变化的温度场中,对受机械载荷作用下的四边简支功能梯度材料柱面曲板的非线性振动特性进行了分析。假设柱面曲板上表面为陶瓷层,下表面为金属层,材料特性为沿厚度方向按幂律梯度变化。在考虑几何非线性与剪切变形情况下,运用一阶剪切变形理论和Hamilton原理建立了功能梯度材料柱面曲板的非线性动力学方程。并用Galerkin法将运动控制方程离散为5个自由度的非线性动力学系统,方程中保留了面内和转动惯性项的影响,利用数值分析方法,研究了在一定横向激励作用下,不同体积分数指数对圆柱壳的非线性动力行为的影响。结果表明,随着材料体积分数指数的增加,曲板的横向振幅和振动速度渐降低。
The nonlinear vibration characteristics of a cylindrical curved plate with simply supported functionally graded material under mechanical loading are analyzed in a temperature field that varies linearly along the thickness. Assume that the surface of the cylindrical curved plate is a ceramic layer and the lower surface is a metal layer, and the material properties change according to a power law gradient along the thickness direction. Considering the geometric nonlinearity and the shear deformation, the nonlinear dynamic equations of a cylindrical curved plate with functionally graded material are established by using the first-order shear deformation theory and the Hamilton principle. And the Galerkin method is used to separate the motion control equation into five degrees of freedom non-linear dynamical system. The influence of in-plane and rotational inertia is retained in this equation. Numerical analysis is used to study the effects of different volume fraction The Influence of Index on Nonlinear Dynamic Behavior of Cylindrical Shells. The results show that with the increase of material volume fraction index, the lateral amplitude and vibration velocity of curved plate decrease gradually.