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Mathematical and numerical modelling of piezoelectric sensors

Published online by Cambridge University Press:  03 February 2012

Sebastien Imperiale  and
Patrick Joly
Sebastien Imperiale
Affiliation:
CEA, List, Saclay, 91191 Gif-sur-Yvette, France. sebastien.imperiale@inria.fr INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, 78153 Le Chesnay, France; patrick.joly@inria.fr
Patrick Joly
Affiliation:
INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, 78153 Le Chesnay, France; patrick.joly@inria.fr
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Abstract

The present work aims at proposing a rigorous analysis of the mathematical and numerical modelling of ultrasonic piezoelectric sensors. This includes the well-posedness of the final model, the rigorous justification of the underlying approximation and the design and analysis of numerical methods. More precisely, we first justify mathematically the classical quasi-static approximation that reduces the electric unknowns to a scalar electric potential. We next justify the reduction of the computation of this electric potential to the piezoelectric domains only. Particular attention is devoted to the different boundary conditions used to model the emission and reception regimes of the sensor. Finally, an energy preserving finite element/finite difference numerical scheme is developed; its stability is analyzed and numerical results are presented.

Keywords

Piezoelectricityquasi-static approximationultrasonic sensors
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 4 , July 2012 , pp. 875 - 909
Copyright
© EDP Sciences, SMAI, 2012

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