☆ 4.1 Article

Development of an improved mathematical model for the dynamic response of a sphere located at a viscoelastic medium interface

EUROPEAN JOURNAL OF PHYSICS (2022)

Journal

EUROPEAN JOURNAL OF PHYSICS

Volume 43, Issue 2, Pages -

Publisher

IOP Publishing Ltd

DOI: 10.1088/1361-6404/ac4647

Keywords

interface; sphere; large oscillation; modified Hertz model; radiation damping; viscosity; viscoelastic medium

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Abstract

This study comprehensively investigates the static and dynamic responses of a sphere located at elastic and viscoelastic medium interfaces. Mathematical models for predicting the static displacement of a sphere at an elastic interface are compared, and an accurate mathematical model for the static displacement of a sphere at an elastic interface is proposed. An improved mathematical model for the dynamic response of a sphere at a viscoelastic interface is developed, considering various factors such as Young's modulus, density, viscosity, and radiation damping. The model provides insights into the dynamic responses of spheres at viscoelastic interfaces, and is a valuable tool for researchers in engineering, materials science, and physics.

A comprehensive investigation on the static and dynamic responses of a sphere located at elastic and viscoelastic medium interfaces is performed in this study. First, the mathematical models commonly used for predicting the static displacement of a sphere located at an elastic medium interface are presented and their performances are compared. After that, based on the finite element analyses, an accurate mathematical model to predict the static displacement of a sphere located at an elastic medium interface valid for different Poisson's ratios of the medium and small and large sphere displacements is proposed. Then, an improved mathematical model for the dynamic response of a sphere located at a viscoelastic medium interface is developed. In addition to the Young's modulus of the medium and the radius of the sphere, the model takes into account the density, Poisson's ratio and viscosity of the medium, the mass of the sphere and the radiation damping. The effects of the radiation damping, the Young's modulus, density and viscosity of the medium and the density of the sphere on the dynamic response of the sphere located at a viscoelastic medium interface are explored. The developed model can be used to understand the dynamic responses of spherical objects located at viscoelastic medium interfaces in practical applications. Furthermore, the proposed model is a significant tool for graduate students and researchers in the fields of engineering, materials science and physics to gain insight into the dynamic responses of spheres located at viscoelastic medium interfaces.

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