Free vibration of thick isotropic and laminated beams with arbitrary boundary conditions via unified formulation and Ritz method

Abstract

• Free vibration of thick rectangular beams with arbitrary boundary conditions. • The Carrera Unified Formulation is used. • The eigenvalue equation is obtained employing the Ritz method . • The results are validated using a 3D finite element solution . • Accurate results are obtained, especially for the first mode of vibration . This paper presents an approximate solution for the free vibration of thick rectangular isotropic and laminated beams with arbitrary boundary conditions. The Carrera Unified Formulation is used in order to consider displacement theories of arbitrary order. The eigenvalue equation is obtained by minimizing an energy functional and the Ritz method is employed to approximate the displacement field. The functions used in the Ritz series can be accommodated to account for any of the classical boundary conditions. The results are validated by studying the convergence behavior and comparing the results with a 3D finite element solution. Natural frequencies are obtained for a variety of boundary conditions and length-to-thickness ratios. Accurate results are obtained, especially for the first mode of vibration which is the most important from an engineering perspective.