Chaotic vibrations of nonlinear viscoelastic plate with fractional derivative model and subjected to parametric and external excitations

Abstract

This paper deals with the analysis of chaotic vibrations of simply supported nonlinear viscoelastic plate with fractional derivative model and subjected to parametric and external excitations. The Galerkin decomposition is used to obtain the modal equation of the system. Using the Melnikov’s theorem, the criterion for appearance of horseshoes chaos from homoclinic bifurcation is presented. The Melnikov’s predictions are confirmed by using the numerical simulation based on the basin of attraction of initial conditions. It is observed that the region of regular motions increases with the fractional order and decreases with the amplitude of parametric excitation. Moreover, it is found that the increase of the viscoelastic parameter contributes to control the chaos. The bifurcation diagrams and maximal Lyapunov exponent are used to show how the system parameters can affect the dissipative chaos.