Forced non-linear vibrations of a damped sandwich beam

Abstract

Forced, damped, non-linear, low-frequency flexural motions of a clamped-clamped sandwich beam with thin face sheets and a soft viscoelastic core are examined experimentally and theoretically. The theory employed neglects the extensional rigidity of the core and treats the face sheets as membranes. The non-linearity stems from axial stretching of the face sheets. Damping is taken into account by modeling the core as a Kelvin solid, with the material parameters used being obtained experimentally as functions of frequency and temperature. Theoretical frequency-amplitude relations are obtained using Galerkin's procedure and the method of harmonic balance. Results on fundamental natural frequencies, mode shapes, and stability are also presented. In the experiment, mechanical contact with the specimen was avoided by employing electromagnetic forcing and using a proximeter to measure displacements. Also, special attention was given to the interface bonds and to the reproduction, as close as possible, of clamped-clamped conditions. Agreement between the theoretical and experimental results is, in general, quite good.