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Monagan, M.B., Geddes, K.O., Heal, K.M., Labahn, G., Vorkoetter, S.M., McCarron, J. and DeMarco, P. (2005) Maple 10 Programming Guide. Maplesoft, Waterloo, ON, Canada.

has been cited by the following article:

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

  AUTHORS: Naum M. Khutoryansky, Vladimir Genis

  KEYWORDS: Piezoelectric Layer, Transient Dynamic Problems, Time Domain Solutions, Green’s Function Method, Nonlinear Boundary Conditions, Nonlinear Damper, Output Voltage

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.5 No.4, April 30, 2017

  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 derived 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.