Symplectic solution for the bending of annular sector plate in circumferential direction

The bending of annular sector plates is investigated withthe symplectic solution in this paper. On the analogy between planeelasticity and plate bending theory, moment functions of plate bending inpolar coordinates are introduced as original variables to establish asymplectic space in circumferential direction for the bending of annularsector plate with an appropriate definition of symplectic innerproduct. With the application of the Pro-Hellinger-Reissner variationalprinciple, dual equations in the symplectic space are yielded to present ananalytical method for the bending of annular sector plates. Moreover, twocases of the symplectic eigenvalue problems are presented: one is for theplate simply supported on the two arc sides, the other for the arccantilever plate.. The transcendental equations of the eigenvalues and theireigenvectors are obtained. The comparison between the theoretical results inthe paper and in other literatures shows a good convergence and accuracy ofthe symplectic solution.