I am looking for an analytical closed form solution for the attached differential equations. The equations are equations of motion and electrostatic potential.
There are solutions for specific cases and there is a solution for an isotropic elastic material in which c's are replaced by Lame constants and Helmholtz decomposition is used. Solutions for the case of axisymmetric loading are available. If you can provide solution for the case of isotropic elastic and radially polarized piezoelectric material then it would be great.
I am attaching an example but for z axis piezoelectric polarized. This work is for a radially polarized one