Transverse vibration of slender sandwich beams with viscoelastic inner layer via a Galerkin-type state-space approach.

Abstract

A novel state-space model for studying free and forced transverse vibrations of sandwich beams, made of two outer elastic beams of the same length, continuously joined by an inner shear-type viscoelastic layer, is presented. The proposed technique enables one to consider: i) inhomogeneous systems; ii) any boundary conditions; and iii) rate-dependent constitutive laws for the inner layer, which can be represented either through Generalised Maxwell's model or Laguerre's Polynomial Approximation. For the viscoelastic model of the inner layer, the dynamic behaviour is described by the Standard Linear Solid model, which is made of a primary elastic spring in parallel with a Maxwell's element. The kinematics of the outer beams is developed by means of Galerkin-type approximations for the fields of both axial and transverse displacements in the outer beams, and imposing the pertinent compatibility conditions at interface. In the proposed formulation, the assumed modes are selected as the first modes of axial vibration and of lateral buckling for each layer with homogenised mechanical properties and their own boundary conditions. Numerical examples using a novel direct integration method for calculating the response of the dynamic system demonstrate the accuracy and versatility of the proposed formulation, in both frequency- and time-domain analyses.