Transient longitudinal waves on impact excited viscoelastic rods with lateral inertia

Abstract

An analytical and numerical Fourier transform based approach is presented to investigate the space-time dependence for the longitudinal velocity resulting from the longitudinal impact force excitation of viscoelastic rods with lateral inertia. A one-dimensional dissipative Rayleigh-Love wave equation including material memory, dissipation, and/or transverse effects due to Poisson coupling is developed from a generic model of the time dependent stress strain relationship for the rod material. A Gaussian signal with a suitable time scale is used to represent the hammer impact forces. Fourier transform, standing wave, and modal methods are utilized to develop analytical solutions for the longitudinal velocity resulting from the impact excitation of semi-infinite and finite length free-free elastic rods with no transverse effects to provide a baseline and segue to analogous results for viscoelastic rods with transverse effects. Numerical results from an FFT approach are presented to illustrate the effects of material losses and transverse effects on attenuation and dispersion in viscoelastic rods using the Kelvin-Voigt model for the constitutive equation of the rods.