High frequency vibration of a rectangular micropolar beam: A dynamical analysis

• This paper deals with the high frequency vibration of a rectangular micropolar beam.
• A new methodology based Hamiltonian principle with Legendre׳s transformation.
• It is reduce the complexities of the problem.
• This micropolar beam model can be easily reduced to Timoshenko beam model in classical case.

The present paper deals with the dynamical solution of a rectangular micropolar beam in high frequency domain. Analogous to symplectic approach by W. Zhong, a new methodology is adopted to solve the vibrational problem by using Hamiltonian principle with Legendre׳s transformation. This paper extends the symplectic elasticity approach and dual variables to a different version that simplifies the solution procedure.