Analysis of the Primary and Secondary Resonances of Viscoelastic Beams Made of Zener Material

Abstract

The problem of geometrically nonlinear, steady-state vibrations of beams made of viscoelastic (VE) materials is considered in this paper. The Euler–Bernoulli and the von Kármán theories are used to describe the dynamic behavior of beams. The VE material of the beams is modeled using the Zener model. Two harmonics are present in the assumed steady-state solution of the problem at hand, which enables an analysis of both the primary and secondary resonances. The virtual work equation and the harmonic balance method are used to derive the amplitude equations in the explicit form. The response curves are determined using the continuation method and treating the frequency of excitation as the main parameter. The results of several examples, which illustrate the dynamic behavior of the considered beams, are presented and discussed.