EXACT THREE DIMENSIONAL ANALYSIS OF THE STABILITY OF LAMINATED TRANSVERSELY ISOTROPIC PIEZOELECTRIC RECTANGULAR PLATES
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摘要: 从横观各向同性压电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,使原方程解耦成两个低阶方程,有利于具体问题的求解。对于四边简支压电层合矩形板面内双向均匀受压的稳定问题,建立了层合板上下表面状态变量间的关系式,利用边界条件进一步导出特征方程。发现存在两类彼此无关的稳定形式:第一类对应板的纯面内稳定,而第二类则是一般意义上的板的弯曲稳定。给出了数值结果,并考察了相关参数的影响。Abstract: By introducing two displacement functions and two stress functions, two independent state equations are constructed based on the three-dimensional piezoelasticity 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 subjected to bi-axial uniform pressures, two relations between the state variables at the top and bottom surfaces are established. In particular, it is found that there exist two independent classes of stabilities. The first class corresponds to the purely in-plane stability and the second to the general flexural stability. Numerical examples are finally presented and the effects of some parameters are discussed.
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