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根据Hamilton原理建立了三维压电压磁动力学耦合系统的Hamilton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Hamilton正则方程组,实现了电磁弹性固体三维问题从欧几里得空间向辛几何空间、从拉格朗日体系向哈密顿体系的过渡。以三维夹层功能梯度压电压磁材料(FGMM)板/管为例,研究了压电压磁耦合系统的静动力学特性,并通过辛算法进行了数值分析。结果表明,FGMM多层板/管结构在横向压力作用下,层间界面附近位移、电势和磁势等物理量连续,而板内应力、电位移和磁感应强度等物理量则出现突变;压电效应对结构的动态刚度起到增大的效果,压磁效应降低了结构的动态刚度。
According to the Hamilton principle, a Hamilton dual system of three-dimensional piezoelectric-piezomagnetic coupling system is established. The classical class of variables in elasticity is transformed into two types of variables. Hamilton positive equations are established, and the three- Griffin space to symplectic geometry, the transition from the Lagrange system to the Hamiltonian system. Taking the three-dimensional FGML plate / tube as an example, the static and dynamic characteristics of the piezomagnetic coupling system are studied and the numerical analysis is carried out by the symplectic algorithm. The results show that physical properties such as displacement, potential and magnetic potential are continuous in the FGMM multilayer plate / tube structure under lateral pressure, and physical parameters such as in-plane stress, electrical displacement and magnetic flux density change abruptly. The piezoelectric effect The dynamic stiffness of the structure plays an increasing role, and the piezomagnetic effect reduces the dynamic stiffness of the structure.