单向轴压下压电矩形薄板的动态后屈曲问题

Dynamic post-buckling of piezoelectric rectangular thin plate under unilateral axially-pressure

利用基于5自由度一阶剪切变形和von Karman几何非线性应变的压电薄板理论,通过双重Fourier级数展开、Galerkin方法和多尺度方法,获得单向轴压和简支边界条件下压电矩形薄板动态后屈曲问题的解析解。给出了压电薄板动态后屈曲的共振特性曲线,对动态后屈曲的跳跃现象进行了研究。数值分析表明,几何参数和材料参数都对压电板的跳跃特性有显著影响。

In order to deal with dynamic post buckling problem of piezoelectric thin plate, a nonlinear piezoelectric thin plate theory which is based on first order shear deformation theory with five freedoms and von Karman geometry nonlinear strain theory is applied. By taking the first natural mode of the plate as the post buckling one, expanding stress function as the double Fourier series, performing the Galerkin procedure and carrying out the Multiple scale method, the exact solution of the non-linear dynamic post-buckling problem of transversely isotropic piezoelectric rectangular thin plates under simply supported boundary conditions and unilateral axially-pressure is obtained. The nonlinear resonance curves of dynamic post buckling of piezoelectric thin plate are presented to study the jumping phenomena. Numerical results show that the effects of the material and geometry parameters on the characteristics of dynamic post-buckling are observably large.