| Issue |
ESAIM: M2AN
Volume 46, Number 4, July-August 2012
|
|
|---|---|---|
| Page(s) | 875 - 909 | |
| DOI | https://doi.org/10.1051/m2an/2011070 | |
| Published online | 03 February 2012 | |
Mathematical and numerical modelling of piezoelectric sensors
1 CEA, List, Saclay, 91191 Gif-sur-Yvette, France
sebastien.imperiale@inria.fr
2 INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, 78153 Le Chesnay, France
patrick.joly@inria.fr
Received: 25 January 2011
Revised: 8 July 2011
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.
Mathematics Subject Classification: 35L05 / 35A35 / 73R05 / 35A40
Key words: Piezoelectricity / quasi-static approximation / ultrasonic sensors
© EDP Sciences, SMAI, 2012
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