The Presence of Chaos in a Viscoelastic Harmonically Forced Von Mises Truss

Abstract

Abstract This paper examines the effect of viscoelasticity on the dynamic behavior of a bistable dome-shaped structure represented as a lumped parameter viscoelastic von Mises truss. The viscoelastic system is governed by a third order jerk equation. The presence of viscoelasticity also introduces additional time scales and degrees of freedom into the problem when compared to their viscous counterparts, thus making the study of these systems in the presence of harmonic loading even more interesting. It is highly likely that the system would exhibit non-regular behavior for some combination of forcing frequency and forcing amplitude. With this motivation, we start by studying the dynamics of a harmonically forced von Mises truss in the presence of viscous damping only. This leads to a Duffing type equation with an additional quadratic non-linearity. We demonstrate some of the rich dynamic behavior that this system exhibits in some parameter ranges. This provides useful insight into the possible behavior of the viscoelastic system. The viscous damper is then replaced by a viscoelastic unit. We show that the system can exhibit both regular as well as chaotic behavior. The threshold limit for the chaotic motion has been determined using Melnikov’s criteria and verified through numerical simulations using the largest Lyapunov exponent.