On nonlinear damping effects with nonlinear temperature-dependent properties for an axial thermo-viscoelastic rod

Abstract

The present manuscript develops a new axisymmetric model of thermo-viscoelastic rods to account for uniform temperature effects and nonlinear terms, which are induced by Kelvin–Voigt damping. A fundamental relationship between the damping of viscoelastic material and nonlinear geometry are researched through the application of Galerkin and multiple scale (MS) methods to the new model. Then, the MSM-based solutions are confirmed with a numerical integration method, and a good agreement between the approximate analytical and numerical results is observed. Free axial vibrations based on the standard linear solid model in uniform thermal rises with nonlinear material properties as a function of temperature is considered. The temperature of the viscoelastic rod remains constant under conditions of uniform temperature rise. Studying the behavior of the dynamic system in the presence of uniform temperatures increases the effect of nonlinear damping on its vibration behavior. Approximate analytical results are presented for use as a reference point in future analysis of nonlinear thermo-viscoelastic rods with a weak hardening system. Also, the results of this research can be useful and practical for finding the modal damping ratio of the system as well as the dynamic analysis of damping in the presence of thermal environment.