The general solution for dynamical problem of rectangular micro-polar beam vibrating at high frequency

In this paper we have made an attempt to find a general solution of a problem of high frequency vibration in a micro-polar rectangular beam. We model the micro-polar beam problem in such a way that it can be reduced to Timoshenko beam problem in classical case. To solve the problem we adopted a methodology based on Hamiltonian principle with Legendre's transformation similar to symplectic approach. It was first applied in elasticity problem in the early 1990s by Professor W. Zhong. After achieving the Hamiltonian formulation for micro-polar beam problem we no longer follow the derivation procedure of symplectic approach but make our own way to solve it in order to reduce the complexities of the problem.