Transverse vibrations of viscoelastic sandwich beams via a Galerkin-based state-space approach

A new state-space model is formulated for the dynamic analysis of sandwich beams that are made of two thin elastic layers continuously joined by a shear-type viscoelastic (VE) core. The model can accommodate different boundary conditions for each outer layer and accounts for the rate-dependent constitutive law of the core through additional state variables. The mathematical derivation is presented with the Standard Linear Solid (SLS) model (i.e., a primary elastic spring in parallel with a single Maxwell element) and then extended to the generalized Maxwell (GM) model. The kinematics equations are developed by means of Galerkin-type approximations for the fields of axial and transverse displacements in the outer layers, and imposing the pertinent compatibility conditions at the interface with the core. Numerical examples demonstrate the accuracy and versatility of the proposed approach, which endeavors to represent the effects of the VE memory on the vibration of composite beams.