Damping analysis of partially covered sandwich beams

Abstract

Two formulations based on simplified methods and one based on an exact method are developed for damping analysis of a partially covered sandwich beam. In the first formulation, an expression for the modal system loss factor is derived as the ratio of energy dissipated per cycle to the maximum strain energy during a cycle of harmonic motion, the modes of vibration being assumed to be the same as that of the base beam. In the second formulation, the analysis is carried out by a Rayleigh-Ritz method. The mode shapes satisfying the boundary conditions are assumed in forms with unknown coefficients, leading to the complex eigenvalues defining the resonance frequencies and the associated modal system loss factors. In the third formulation, the classical Euler beam theory for the uncovered portion of the beam, and for the sandwich beam the theory for the covered portion, with continuity conditions at the common sections, have been used. The formulation based on the first method gives the modal system loss factors only while the Rayleigh-Ritz and classical methods give the modal system loss factors as well as the associated resonance frequencies. The classical approach is an exact method but because it involves a two-variable search technique takes a much longer computation time to achieve accurate results.