Electromagnetoelastic Dynamic Response of Transversely Isotropic Piezoelectric Hollow Spheres in a Uniform Magnetic Field

Abstract

An analytical method is presented to solve the problem of electromagnetoelastic dynamic response of transversely isotropic piezoelectric hollow spheres in a uniform magnetic field, subjected to arbitrary mechanical load and electric excitation. Exact expressions for the dynamic responses of stresses, perturbation of magnetic field vector, electric displacement, and electric potential in piezoelectric hollow spheres are obtained by means of Hankel transform, Laplace transform and their inverse transforms. An interpolation method is applied to solve the Volterra integral equation of the second kind involved in the exact expression, which is caused by interaction between electric-elastic field and electric-magnetic field. Thus, an analytical solution for the problem of dynamic response of a transversely isotropic piezoelectric hollow sphere in a uniform magnetic field is obtained. Finally, some numerical examples are carried out, and may be used as a reference to solve other dynamic coupled problems of electromagneto-elasticity.