Abstract
This paper presents an analytical method for solving both the free and forced vibration of an axially loaded stepped laminated beam with general layers and arbitrary boundary conditions based on the first-order shear deformation theory (FSDT). The beam is divided into appropriate segments and the spectral element matrix is employed to formulate the solutions for each segment. The transfer matrix method is adopted to analytically combine the solutions and boundary conditions of each segment. The solutions to the free and forced vibration of the beam are then obtained by solving a 6 × 6 matrix equation. The results obtained by the proposed method show good agreement with those by the finite element method (FEM). Parametric studies are presented to study the effect of beam parameters on the dynamic characteristics of the beams.
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