压电、压磁耦合弹性介质圆板的自由振动

The free vibration of the circular plate for the piezoelectric-piezomagneto and elastic media

依据横观各向同性压电、压磁耦合弹性介质材料的动力学方程,导出了压电、压磁弹性圆板在轴对称变形下的状态变量方程,在给定的边界条件下,通过Caylay-Hamilton原理和利用传递矩阵方法,导出了单层和多层压电、压磁耦合弹性介质圆板自由振动的状态变量解.算例表明,得到了在不同情况下板的最低阶频率随板厚跨比的变化规律,得知压电、压磁材料层合板的振动特性与材料的叠层顺序有关.

The fundamental equation of vibration for transversely isotropic piezoelectric, piezomagnetic and e-lastic media is observed. The state vector equation of transversely isotropic space axial symmetric problem in piezoelectric , piezomagnetic and elastic media is established. According to the theory of ordinary differential e-quations and the Caylay-Hamilton theorem under the boundary conditions, the solutions of state vector equation of free vibration for the circular plate with simply supported edges are obtained which are the product of initial state variables and transfer matrix. The general formulation of the solution for thick laminated circular plate of piezoelectric、piezomagnetic and elastic media is given using the method of transfer matrix.