横观各向同性层合矩形板弯曲、振动和稳定的三维精确分析

针对四边简支的横观各向同性矩形板的弯曲、振动和稳定给出了新的状态空间分析方法。从横观各向同性弹性力学的三维基本方程出发，通过引入位移函数和应力函数，构造了两类相互独立的状态空间方程，不仅使原方程得到解耦而且降低了阶数，十分有利于具体问题的求解。对于四边简支的矩形板，建立了层合板上下表面状态变量间的关系式。特别针对矩形板的自由振动（稳定）问题，发现存在两类彼此无关的形式，一类对应板的纯面内振动（稳定），而另一类则是一般意义上的板的弯曲振动（稳定）。给出了数值结果，并考察了相关参数的影响。

On the Bending, Vibration and Stability of Laminated Rectangular Plates With Transversely Isotropic Layers

A method based on newly presented state space formulations is developed for analyzing the bending, vibration and stability of laminated transversely isotropic rectangular plates with simply supported edges. By introducing two displacement functions and two stress functions, two independent state equations were constructed based on the three_dimensional elasticity equations for transverse isotropy. The original differential equations are thus decoupled with the order reduced that will facilitate obtaining solutions of various problems. For the simply supported rectangular plate, two relations between the state variables at the top and bottom surfaces were established. In particular, for the free vibration (stability) problem, it is found that there exist two independent classes: One corresponds to the pure in_plane vibration (stability) and the other to the general bending vibration (stability). Numerical examples are finally presented and the effects of some parameters are discussed.