An accurate and straightforward approach to thermo-electro-mechanical vibration of piezoelectric fiber-reinforced composite cylindrical shells

Abstract

Exact solutions for thermo-electro-mechanical free vibration of a piezoelectric fiber-reinforced composite (PFRC) cylindrical shell is obtained under the framework of Hamiltonian mechanics. Two types of fiber reinforcement including the uniformly distributed in each ply and functionally graded in the thickness direction are taken into considered. Unlike the classical analytical treatment which relies on trial functions, the governing equations in the Hamiltonian form can be directly solved through a rigorous way. Free vibration of PFRC cylindrical shells is reduced into a symplectic eigenproblem which has five kinds of explicit eigenfunctions. Analytical frequency equations and vibration mode shapes are derived simultaneously. In numerical examples, a comparison study is performed to verify the validity of the proposed solution. A detailed discussion is presented to reveal the effects of key influencing factors on the expression of eigenfunctions. Some new results which can be used as benchmarks for the approximate approach are given also.