Modelling of finite piezoelectric patches: Comparing an approximate power series expansion theory with exact theory

Abstract

a b s t r a c tPlate equations for a plate consisting of one elastic layer and one piezoelectric layer with an applied electric voltage have previously been derived by use of power series expansions of the field variables in the thickness coordinate. These plate equations are here evaluated by the consideration of a time harmonic 2D vibration problem with finite layers. The boundary conditions at the sides of the layers then have to be considered. Numerical comparisons of the displacement field are made with solutions from two other theories; a solution with equivalent boundary conditions for a thin piezoelectric layer applied on an elastic plate and an exact solution based on Fourier series expansions. The two approximate theories are shown to be equally good and they both yield accurate results for low frequencies and thin plates.

Nonlinear Mechanics of Thin-Walled Structures

“…Thus, Goldenveizer [64] obtained two-dimensional equations for the leading terms of the solution for a homogeneous plate; in [105] his asymptotic method with a change of unknowns was applied to the analysis of an electromechanically coupled problem. An asymptotic study, in which the substrate and the piezoelectric layers of the plate are considered explicitly with piecewise solutions and conditions on the interfaces between the layers, is presented in [106]. An asymptotic study, in which the substrate and the piezoelectric layers of the plate are considered explicitly with piecewise solutions and conditions on the interfaces between the layers, is presented in [106].…”

Asymptotic splitting in the three-dimensional problem of elasticity for non-homogeneous piezoelectric plates

“…An advanced study of piezoelectric plates with material non-homogeneity in all three dimensions is reported by Kalamkarov and Kolpakov (2001) ; the usage of powerful mathematical techniques, typical for the analysis of periodic structures, makes the latter work quite complicated. An example of an asymptotic analysis, in which the layers of the structural material and piezoelectric material in the plate are considered explicitly with piecewise solutions and conditions on the interfaces between the layers, is presented by Mauritson (2009) .…”

Low-frequency dispersion of fundamental waves in anisotropic piezoelectric plates

“…Also the low-frequency dispersion coefficients are essential ingredients for various asymptotic and engineering plate theories. Much work continues to be done on this subject for piezoelectric plates (see Johansson and Niklasson, 2003;Cheng and Reddy, 2003;Krommer, 2003;Wang and Rokhlin, 2004;Joshi et al, 2006;Mauritsson et al, 2008;Kuznetsova et al, 2008;Mauritsson, 2009). However, there remain certain unexplored aspects, particularly those related to anisotropy.…”