Nonlinear steady state vibrations of beams made of the fractional Zener material using an exponential version of the harmonic balance method

Abstract This paper presents the application of an exponential version harmonic balance method to analysis steady state vibration geometrically nonlinear systems. A detailed description and corresponding numerical procedure is provided. The von Karman theory used describe effects geometric nonlinearity. material beams modelled with help Zener model using fractional calculus. problem solved method. In above-mentioned version, complex calculus in contrast ordinary method, where vibrations are described trigonometric functions. It significantly simplifies derivation amplitude equations. Moreover, more elegant comparison one. equations presented. modified continuation proposed solve determine response curves. results exemplary calculation presented compared known order justify efficiency correctness approach.