横观各向同性功能梯度材料矩形板的自由振动

考察了沿厚度方向材料和为非均匀的功能梯度横观各向同性矩形板的自由振动。通过引入两个位移函数和两个应力函数导出了两个独立的变系数状态方程，进一步利用分层反似理论，将变系数状态方程为常纱数状态方程并求解，发现存在两类的自由振动形式：第一类对应纯板内振动，第二类对应一般的弯曲振动。给出了数值结果，讨论了材料梯度指标对固有频率的影响。

Free Vibration of Transversely Isotropic FGM Rectangular Plates

The free vibration of a transversely isotropic and functionally graded rectangular plate with material constanting inhomogeneous across thickness is investigated in the paper. By introducing two displacement functions and two stress functions, two independent state equations with varying coefficients are derived. Laminarized approximation is then used so that the state equations are treated as the ones with constant coefficients in each sub layer, the solutions of which are easily obtained. It is found that there are two independent patterns of vibration. One corresponds to the pure in plane vibration and the other to the general bending vibrtation. Numerical results are presented and the effect of the material gradient index on the natural frequencies is discussed.