The Mixed Energy Hamilton Variational Rinciples And Biorthogonality Relationships For Some Elasticity Problems

Separable and linear Hamiltonian systems which have good structural characteristics have many explicit numerical methods. The Hamiltonian variational principles are ob-tained and biorthogonal relationships of the eigenfunctions are established according to the separable Hamilton system. By constructing new dual variables and using the equiv-alence between the integral form and differential form of the separable Hamilton system, the mixed energy Hamilton variational principles are obtained and intrinsic relationships between the two principles are explained in some aspects that include the disturbance problem of plane viscous flow, the Mindlin plate bending problem, the problem of forced vibration of orthotropic thin plates and the natural vibration of circular and annular thin plates problem. Furthermore, the biorthogonal relationships of the eigenfunctions are established. At last, the result verifies the validity of the proposed approach.