Dynamic characteristics of multilayered beams with viscoelastic layers described by the fractional Zener model

Abstract

This paper concerns the dynamic analysis of composite beams containing elastic and viscoelastic (VE) layers. A method for determination of the dynamic characteristics of multilayered beams with VE layers (i.e., natural frequencies, non-dimensional damping ratios and modes of vibration) is presented. The Euler–Bernoulli beam theory and the Timoshenko theory are used to describe the elastic and VE layers, respectively. To describe the mechanical properties of a VE layer, the four-parameter rheological model with fractional derivative is applied. A number of particular rheological models are particular cases of this general model. The virtual work principle and the finite element method together with the Laplace transform are used to derive the equation of motion in the frequency domain. The dynamic characteristics of a beam with VE layers are obtained as the solution to a properly defined nonlinear eigenvalue problem. The continuation method is adopted for solving the nonlinear eigenproblem. Several conclusions concerning the accuracy of the method and variability of results are presented on the basis of numerical studies.