横观各向同性压电矩形薄板的非线性振动

Nonlinear Vibration of Transversely Isotropic Piezoelectric Rectangular Plate

由于压电材料在航空航天轻形结构动力控制中的广泛应用 ,压电结构的非线性机理成为工程界急需解决的问题。为了拓广压电结构的理论基础 ,本文对于横观各向同性压电矩形薄板 ,给出了大挠度条件下的应变位移关系 ,利用 Hamilton原理导出了压电矩形薄板的非线性振动方程 ,并用双重 Fourier级数展开和 Galerkin方法获得四边简支压电矩形薄板非线性自由振动的解析解 ,分析了材料参数和几何参数对振动特性的影响。

Piezoelectric elements integrated with conventional elastic structure used as either sensor or actuator for structural identification and control play key roles as active components in 'smart' structure system. Thus, a comprehensive and thorough understanding of nonlinear behaviors of piezoelectric structures is urgently required for engineering application. To broaden the theoretical fundamental of piezoelectric structures, the geometrically nonlinear relation between strain and displacement of a transversely isotropic piezoelectric rectangular plate is proposed and basic large deformation equations are established. General nonlinear vibration equations of transversely isotropic piezoelectric rectangular plate are formulated using Hamilton′s principle. General electric and mechanical boundary conditions are derived. By applying the double Fourier series as the displacement mode and performing the Galerkin procedure, the exact solution of the free vibration of transversely isotropic piezoelectric rectangular plates is obtained under simply supported boundary conditions. The effects of parameters of the material and geometry on the characteristics of the vibrations are analyzed.