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A finite element model for nonlinear behaviour of piezoceramics under weak electric fields

Samal, M. K. and Seshu, P. and Parashar, S. and von Wagner, U. and Hagedorn, Peter and Dutta, B. K. and Kushwaha, H. S. (2005):
A finite element model for nonlinear behaviour of piezoceramics under weak electric fields.
41, In: Finite Elements in Analysis and Design, (15), pp. 1464-1480, [Online-Edition: http://www.sciencedirect.com/science/article/B6V36-4GHRBTX-1...],
[Article]

Abstract

It has been experimentally observed that piezoceramic materials exhibit different types of nonlinearities under different combinations of electric and mechanical fields. When excited near resonance in the presence of weak e to a Duffinor such as jump phenomena and presence of superharmonics in the response spectra. There has not been much work in the litrature to model these types of nonlinearities. Some authors have developed one-dimensional models for the above phenomenon and derived closed-form solutions for the displacement response of piezo-actuators. However, the generalized three-dimensional (3-D) formulation of electric enthalpy, the variational formulation and the FEM implementation have not yet been addressed, which are the focus of this paper. In this work, these nonlinearities have been modelled in a 3-D piezoelectric continuum using higher order quadratic and cubic terms in the generalized electric enthalpy density function. The coupled nonlinear finite element equations have been derived using variational formulation. A special linearization technique for assembling the nonlinear matrices and solution of the resulting nonlinear equations has been developed. The method has been used for simulating the nonlinear frequency response of a lead zirconate titanate plate excited near its first in-plane vibration resonance frequency with sinusoidal excitations of different electric field strengths. The results have been compared with those of the experiment.

Item Type: Article
Erschienen: 2005
Creators: Samal, M. K. and Seshu, P. and Parashar, S. and von Wagner, U. and Hagedorn, Peter and Dutta, B. K. and Kushwaha, H. S.
Title: A finite element model for nonlinear behaviour of piezoceramics under weak electric fields
Language: English
Abstract:

It has been experimentally observed that piezoceramic materials exhibit different types of nonlinearities under different combinations of electric and mechanical fields. When excited near resonance in the presence of weak e to a Duffinor such as jump phenomena and presence of superharmonics in the response spectra. There has not been much work in the litrature to model these types of nonlinearities. Some authors have developed one-dimensional models for the above phenomenon and derived closed-form solutions for the displacement response of piezo-actuators. However, the generalized three-dimensional (3-D) formulation of electric enthalpy, the variational formulation and the FEM implementation have not yet been addressed, which are the focus of this paper. In this work, these nonlinearities have been modelled in a 3-D piezoelectric continuum using higher order quadratic and cubic terms in the generalized electric enthalpy density function. The coupled nonlinear finite element equations have been derived using variational formulation. A special linearization technique for assembling the nonlinear matrices and solution of the resulting nonlinear equations has been developed. The method has been used for simulating the nonlinear frequency response of a lead zirconate titanate plate excited near its first in-plane vibration resonance frequency with sinusoidal excitations of different electric field strengths. The results have been compared with those of the experiment.

Journal or Publication Title: Finite Elements in Analysis and Design
Volume: 41
Number: 15
Divisions: 16 Department of Mechanical Engineering > Dynamics and Vibrations
16 Department of Mechanical Engineering
Date Deposited: 19 Jan 2009 15:23
Official URL: http://www.sciencedirect.com/science/article/B6V36-4GHRBTX-1...
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