Exact Time Domain Solutions of 1-D Transient Dynamic Piezoelectric Problems with Nonlinear Damper Boundary Conditions

TL;DR

This paper develops exact time domain solutions for 1-D transient piezoelectric problems with nonlinear damper boundary conditions, using a Green's function method and recursive procedures, applicable to various boundary conditions.

Contribution

It introduces a novel exact analytical recursive method for solving nonlinear boundary conditions in 1-D transient piezoelectric problems, including explicit solutions.

Findings

Effective recursive procedure for nonlinear boundary conditions

Explicit exact solutions for specific cases

Illustrative examples of electric potential behavior

Abstract

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.