哈密顿体系下功能梯度压电板/管静动力三维解

根据哈密顿原理建立了三维压电动力学耦合系统的哈密顿对偶体系,将经典的弹性力学一类变量问题转化为二类变量,并建立了哈密顿正则方程组.分别在不同坐标系下研究了功能梯度压电材料FGPM(Functionally Graded Piezoelectric Material)四边简支板及两端简支管的静动力学特性,通过辛算法进行了数值分析.结果表明,在哈密顿对偶体系中能够求解复杂FGPM结构机电耦合静动力学问题;在FGPM多层板/管结构中,面外变量在厚度方向连续分布,而面内变量在材料分界面处存在突变现象.

3D solutions for static/vibration of FGPM plate/pipe in Hamiltonian system

The 3-dimensional couple equations of piezoelectric-mechanic were derived into Hamilton system by the principle of Hamilton theorem.The problem of single sort of variables was converted to double sorts of variables,and the Hamilton canonical equations were established.The dynamic characteristics of the simply supported functionally graded piezoelectric material(FGPM) plate and pipe are investigated in different coordinate systems.Finally,the problem was solved by the symplectic algorithm.The results show that the complex electromechanical problems of FGPM structures can be solved in the Hamiltonian system.The general displacement and stress of the medium are divided into so-called out-of-plane variables and in-plane variables.The former is continuous while the latter is discontinuous along the depth.