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

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

Naum M Khutoryansky and Vladimir Genis
Journal of applied mathematics and physics, v 5(4), pp 873-888
09 May 2017
DOI: https://doi.org/10.4236/jamp.2017.54077
url
http://www.scirp.org/journal/PaperDownload.aspx?paperID=76013View
Published, Version of Record (VoR) Open
url
https://doi.org/10.4236/jamp.2017.54077View
Published, Version of Record (VoR) Open

Abstract

Mathematics - Numerical Analysis
Journal of Applied Mathematics and Physics, 5, 873-888, 2017 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.

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