Vibration and Damping Analysis of Multi-Span Sandwich Beams with Arbitrary Boundary Conditions

Abstract

This paper presents an analytical model for the study of the coupled transverse and longitudinal vibration of multi-span sandwich beam systems with arbitrary boundary conditions. The energy method and Hamilton's principle approach is used to derive the governing equations of motion and the natural and forced boundary condition equations for each span. The shear, longitudinal and transverse strain energy of the adhesive layer are included in the analysis, together with the transverse and the longitudinal inertia of the composite beam system. A matrix equation to obtain the system natural frequencies and loss factors is developed based on the governing equations of motion for individual spans and system boundary and continuity conditions. Possible boundary conditions that can be programmed to obtain numerical solutions are discussed. Numerical results are generated for an example case of a two-span sandwich beam. The effects of the adhesive thickness, location of the intermediate support, operating temperature and the damping material properties on the system resonance frequency and modal loss factor are studied for the example case.