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.
Highlights
Spherical objects, such as bubbles and spheres, embedded in mediums and at viscoelastic interfaces are encountered in many applications [1,2,3]
In practice, for example, in therapeutic and diagnostic ultrasound applications that use microbubbles [5] and in atomic force microscopy or indentation tests that use spheres [6,7,8], the spherical objects are at viscoelastic interfaces
Mathematical models for the displacements of a bubble located at medium interfaces in response to external loads were proposed [10,11] and these models were evaluated experimentally [12]
Summary
Spherical objects, such as bubbles and spheres, embedded in mediums and at viscoelastic interfaces are encountered in many applications [1,2,3]. The model proposed in this study 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
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