【作者】 赵莉； 陈伟球；

【Author】 Li ZHAO,Wei-qiu CHEN Department of Civil Engineering,Zhejiang University,Hangzhou 310058,China

【机构】 浙江省杭州市余杭塘路388号浙江大学土木工程学系；

【摘要】 本文在哈密顿体系下分析横观各向同性功能梯度压电材料的平面问题,考虑沿长度方向材料参数为指数变化,通过引入对偶变量建立相应的状态方程,并求解了特殊本征值的本征解。与均匀压电材料相比,本文利用"移位"Hamilton矩阵的概念,建立起相应的辛共轭正交关系,并把特殊本征值的本征解与均匀材料进行了对比,发现材料的非均匀性使特殊本征解的形式发生了变化。辛方法在问题的求解中能凸显物理意义,可进一步应用于其它功能梯度压电材料问题。更多还原

【Abstract】 This paper applies the symplectic method to solve the plane problem of Functional Graded Piezoelectric Materials(FGPM) whose elastic stiffness,piezoelectric and dielectric constants vary exponentially with the axial coordinate.After introducing the displacements(the electrical potential function) and their conjugate stress(electric displacement),the problem is formulated within the frame of state space and it is solved using the method of separation of variables along with the eigenfunction expansion technique.Compared with that for homogeneous materials,the operator matrix is not in an exact Hamiltonian form,but it has similar properties.This operator matrix is called the shifted-Hamiltonian matrix since the eigenvalues are symmetric with respect to -α/2,rather than zero in the normal Hamilton matrix.In this case,the symplectic adjoint eigenvalue of zero isn’t itself but -α.In this paper the eigensolutions corresponding to zero and -αare gained which indicate certain physical essence of the problem that can not be revealed by other methods. These also can be degenerated to the ones for homogeneous materials after suppressing certain rigid motions.更多还原