  Novel exact solutions of one-dimensional transient dynamic piezoelectric
problems for thickness polarized layers and disks, or length polarized rods,
are obtained. The solutions are obtained using a time domain Green's function
method that leads to an exact analytical recursive procedure which is
applicable for a wide variety of boundary conditions including nonlinear cases.
A nonlinear damper boundary condition is considered in more detail. The
corresponding nonlinear relationship between stresses and velocities at a
current time moment is used in the recursive procedure. In addition to the
exact recursive procedure that is effective for calculations, some new
practically important explicit exact solutions are presented. Several examples
of the time behavior of the output electric potential difference are given to
illustrate the effectiveness of the proposed exact approach.
