Model and solution of impact problem of Timoshenko beam in Hamiltonian system

For the impact problem of Timoshenko beam in Hamiltonian system, the general expression of the full state variables vector composed of displacements and stress is given by making use of the Hamiltonian canonical equations and conjugate symplectic ortho-normalization relationship. And on the basis of this result, the expressions of frequency equations and generalized mode functions are obtained by introducing the boundary conditions to the state variables vector. According to the Hamiltonian canonical equations, the orthogonal relationship between generalized mode function vectors is proved in the form of state variable vector. The numerical results of this problem are given finally. The general method of getting the mathematical model and solution of structural dynamics in Hamiltonian system can be found.