Free Vibration Analysis of Sandwich Beams: A Dynamic Finite Element

The free vibration analysis of three-layered symmetric sandwich beams is studied. The governing differential equations of motion in free vibration are coupled both in axial and bending deformations. The weighted residual method is used and the resulting weak integral form of the governing equations is discretized using the Finite Element Method (FEM) formulation. The dynamic, frequency-dependent, trigonometric shape functions, derived from the solution of the uncoupled equations, are then used to develop the element matrices. The assembly of resulting Dynamic Finite Element (DFE) matrices leads to a nonlinear eigenvalue problem. A determinant search method is then used to compute the coupled natural frequencies and modes of a symmetric, thin face-layer sandwich beam. The DFE numerical results for the first four bending-axial coupled modes, obtained from a 20-element mesh, show good agreement with FEM, exact Dynamic Stiffness Matrix (DSM) method, and other results available in the literature. All the four modes are found to be dominated by bending deformation. The discussion of results is followed by some concluding remarks.