Development of a Model for Predicting Dynamic Response of a Sphere at Viscoelastic Interface: a Dynamic Hertz Model

Abstract

A model for predicting the dynamic response of a sphere at viscoelastic interface is presented. The model is based on Hertz contact model and the model for a sphere in a medium. In addition to the elastic properties of medium and the size of sphere, the model considers the density of sphere, the density and viscosity of medium, and damping of oscillations of sphere due to radiation of shear waves. The model can predict not only the effects of the mechanical properties of medium, the physical properties of sphere, and the amplitude of excitation force on sphere displacement, but also the effects of these parameters on shift of resonance frequency. The proposed model can be used to identify the elastic and damping properties of materials, and to understand the dynamic responses of spherical objects at viscoelastic interfaces in practical applications.