Exact solutions for free vibration analysis of laminated, box and sandwich beams by refined layer-wise theory

Abstract

The present work addresses a closed-form solution for the free vibration analysis of simply supported composite laminated beams via a refined one-dimensional (1D) model, which employs the Carrera Unified Formulation (CUF). In the framework of CUF, the 3D displacement field can be expanded as any order of generic unknown variables over the cross section, in the case of beam theories. Particularly, Lagrange expansions of cross-sectional displacement variables in conjunction with layer-wise (LW) theory are adopted in this analysis, which makes it possible to refine the kinematic fields of complex cross section by arbitrary order and accuracy. As a consequence, the governing equations can be derived using the principle of virtual work in a unified form and can be solved by a Navier-type, closed-form solution. Numerical investigations are carried out to test the performance of this novel method, including composite and sandwich beams ranging from simple to complex configurations of the cross section. The results are compared with those available in the literature as well as the 3D finite element method (FEM) solutions computed by commercial codes. The present CUF model is proved to be able of achieving high accurate results with less computational costs. Besides, they may serve as benchmarks for future assessments in this field.