An Efficient Finite Element for Vibration Analysis of Symmetric Sandwich Beams Subjected to Harmonic Bending Excitations

Abstract

An efficient sandwich beam finite element is developed for the coupled axial bending vibration analysis of sandwich beams subjected to general harmonic bending excitations. A Hamilton’s variational formulation is used to derive the governing field equations, which are exactly resolved to establish the exact solution for dynamic response in steady state form. A set of shape functions is created using the exact solution of the governing equations. These functions are employed to construct a finite element for beams. This finite element features two nodes, each with six degrees of freedom, effectively representing the coupling between the extensional and flexural behaviours of symmetric sandwich beams subjected to harmonic bending loads in static and steady-state dynamic responses. To establish the exactness and effectiveness of the current sandwich beam element, it is compared with established Abaqus finite element solution and other solutions reported in the litrature. The newly developed sandwich beam element demonstrates freedom from discretization errors observed in alternative interpolation methods. It produces results that closely match those obtained from other finite element solutions, but at a significantly reduced computational and modelling cost