Exact Time Domain Solutions of 1-D Transient Dynamic Piezoelectric Problems with Nonlinear Damper Boundary Conditions
Provides exact solutions for piezoelectric problems with nonlinear boundary conditions, which is a niche contribution for researchers in piezoelectricity.
The paper presents exact analytical solutions for 1-D transient dynamic piezoelectric problems with nonlinear damper boundary conditions using a time domain Green's function method. The recursive procedure yields explicit solutions, demonstrated through examples of output electric potential difference.
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.