Exact Electromagnetothermoelastic Solution for a Transversely Isotropic Piezoelectric Hollow Sphere Subjected to Arbitrary Thermal Shock

Abstract

This paper presents analytical study for electromagnetothermoelastic transient behavior of a transversely isotropic hollow sphere, placed in a uniform magnetic field, subjected to arbitrary thermal shock. Exact solutions for the transient responses of stresses, perturbation of magnetic field vector, electric displacement and electric potential in the transversely isotropic piezoelectric hollow sphere are obtained by means of the Hankel transform, the Laplace transform and their inverse transforms. An interpolation method is used to solve the Volterra integral equation of the second kind caused by interactions among electric, magnetic, thermal and elastic fields. From the sample numerical calculations, it is seen that the present method is suitable for the transversely isotropic hollow sphere, placed in a uniform magnetic field, subjected to arbitrary thermal shock. Finally, the result can be used as a reference to solve other transient coupling problems of electromagnetothermoelasticity.