Abstract
In this paper, an analytical solution for the effect of the rotation in a magneto-thermo-viscoelastic non-homogeneous medium with a spherical cavity subjected to periodic loading is presented. The distribution of displacements, temperature, and stresses in the non-homogeneous medium in the context of generalized thermo-elasticity using GL (Green-Lindsay) theory is discussed and obtained in analytical form. The results are displayed graphically to illustrate the effect of rotation, relaxation, magnetic field, viscoelasticity, and non-homogeneity. Comparisons are made with the previous work in the absence of rotation and initial stress.
Highlights
1 Introduction In recent years, the theory of magneto-thermo-viscoelasticity, which deals the interactions among strain, temperature, and electromagnetic fields has drawn the attention of many researchers because of its extensive use in diverse fields, such as geophysics for understanding the effect of the Earth’s magnetic field on seismic waves, damping of acoustic waves in a magnetic field, emission of electromagnetic radiations from nuclear devices, development of a highly sensitive superconducting magnetometer, electrical power engineering, optics, etc.; see [ – ]
Mahmoud et al [, ] investigated the effect of the rotation on plane vibrations in a transversely isotropic infinite hollow cylinder, the effect of the rotation on wave motion through a cylindrical bore in a micropolar porous cubic crystal and he investigated the effect of a magnetic field and non-homogeneity on the radial vibrations in a hollow rotating elastic cylinder
Abd-Alla et al [ – ] investigated the effect of the rotation on a non-homogeneous infinite cylinder of orthotropic material, influence of rotation, radial vibrations in a non-homogeneous orthotropic elastic hollow sphere subjected to rotation, and they investigated the magneto-thermo-elastic problem in a rotating non-homogeneous orthotropic hollow cylinder in the hyperbolic heat conduction model
Summary
The theory of magneto-thermo-viscoelasticity, which deals the interactions among strain, temperature, and electromagnetic fields has drawn the attention of many researchers because of its extensive use in diverse fields, such as geophysics for understanding the effect of the Earth’s magnetic field on seismic waves, damping of acoustic waves in a magnetic field, emission of electromagnetic radiations from nuclear devices, development of a highly sensitive superconducting magnetometer, electrical power engineering, optics, etc.; see [ – ]. Mahmoud [ , ] investigated the analytical solution for an electrostatic potential on wave propagation modeling in human long wet bones, and they studied the influence of rotation and generalized magneto-thermo-elastics on Rayleigh waves in a granular medium under the effect of initial stress and a gravity field. Abd-Alla and Mahmoud [ ] investigated the analytical solution of wave propagation in non-homogeneous orthotropic rotating elastic media. Mukhopadhyay [ ] investigated the effects of thermal relaxations on thermo-viscoelastic interactions in an unbounded body with a spherical cavity subjected to a periodic loading on the boundary. The effects of thermal relaxations on thermo-elastic interactions in an unbounded body with a spherical cavity or cylindrical hole subjected to a periodic loading on the boundary, respectively, were investigated by Roychoudhuri and Mukhopadhyay [ ]. Mahmoud [ ] investigated the analytical solution for free vibrations of an elasto-dynamic orthotropic hollow sphere under the influence of rotation
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