By introduction of a special dependent variable and separation of variables technique, the electroelastic dynamic problem of a nonhomogeneous, spherically isotropic hollow sphere is transformed to a Volterra integral equation of the second kind about a function of time. The equation can be solved by means of the interpolation method, and the solutions for displacements, stresses, electric displacements and electric potential are obtained. The present method is suitable for a piezoelectric hollow sphere with an arbitrary thickness subjected to arbitrary mechanical and electrical loads. Numerical results are presented at the end.
By virtue of the separation of variables technique, the spherically symmetric electroelastic dynamic problem of a spherically isotropic hollow sphere is transformed to an integral equation about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solution of displacements, stresses, electric displacements, and electric potential are obtained. The present method is suitable for a piezoelectric hollow sphere with an arbitrary thickness subjected to spherically symmetric electric potential and radial mechanical loads, that both can be arbitrary functions about the time variable, at the internal and external surfaces.
The elastodynamic solution of a multilayered hollow sphere for spherically symmetric problems is obtained by decomposition into two parts, one being the quasi-static and the other the dynamic solution. The quasi-static solution is firstly derived by means of the state-space method, and the dynamic solution is obtained by utilizing the separation of variables method and the orthotropic expansion technique. The solutions for displacement and stresses are obtained in result. The present method is suitable for a multilayered spherically isotropic hollow sphere, with arbitrary thickness of each of the layers and arbitrary initial conditions, subjected to arbitrary form of a spherically symmetric dynamic load at the internal and external surfaces. Numerical results are finally presented.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.