Following Timoshenko theory of beams and the Hamilton variational principle,a mathematical model of dynamic behavior analysis of nonlinear elastic piles was established,in which three displacements and two angles were contained.

Following the modified theory of beams with the effect of shear deformation,a generalized Hamilton variational principle with three displacements and two rotational angles is established in which the material of pile obeys one of the thrice nonlinear constitutive relations.

Using the Hamiltonian principle and the Galerkin s method, the motion equations of the system were derived.

By using the Hamiltonian principle and the Galerkin s method, the equations of motion of the bladed disk assemblies are derived.

One-field Hamilton-type quasi-variational principle in linear damping elastodynamics of the rigid and elastic supported beam is established which can fully characterize the initial-boundary-value problem of this dynamics.

According to the basic idea of classical yin-yang complementarity and modem dual-complementarity,in a simple and unified way proposed by Luo,the unconventional Hamilton-type incremental variational principles for piece- wise linear elstodynamics of thin plates were established systematically.

Based on energy variation principle,the governing differential equations and the corresponding boundary conditions of box girder with consideration for the shear lag effect and shear deformation as well as rotational inertia were induced.

The energy variation principle is applied to establish the governing differential equations and corresponding natural boundary conditions on the static and dynamic characteristics of thin-walled I-beam, and closed-form solutions of generalized displacements are obtained.