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

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...

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Bibliographic Details
Published in:arXiv.org 2017-05
Main Authors: Khutoryansky, Naum M, Genis, Vladimir
Format: Article
Language:English
Subjects:
Boundary conditions
Disks
Exact solutions
Green's functions
Mathematical analysis
Nonlinear programming
Piezoelectricity
Recursive methods
Thickness
Time domain analysis
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1705.03485