Free vibrations analysis of sandwich beams with viscoelastic core

Abstract

In this work, we treat the problem of free vibrations of sandwich beams with viscoelastic core by considering its frequency dependence. The formulation of the equation of motion is carried out by the Hamilton principle whose Euler-Bernouilli theory is applied to the faces and the Timoshenko theory to the viscoelastic core. The discretization of the bending motion equation is carried out by the finite element methods to obtain the eigenvalues problem corresponding to linear free vibrations. The difficulty of solving the eigenvalues problem due to the frequency dependence of the stiffness matrix leads us to use the asymptotic numerical methodto get the
eigenmodes and the damping properties characterizing the viscoelastic sandwich beam.

Keywords: Vibration, Finite element, Numerical asymptotic, Viscoelastic material, Complex eigenvalues, Damping properties