Mathematical and numerical modelling of piezoelectric sensors

Sebastien Imperiale; Patrick Joly

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 4, page 875-909
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Imperiale, Sebastien, and Joly, Patrick. "Mathematical and numerical modelling of piezoelectric sensors." ESAIM: Mathematical Modelling and Numerical Analysis 46.4 (2012): 875-909. <http://eudml.org/doc/277852>.

@article{Imperiale2012,
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.},
author = {Imperiale, Sebastien, Joly, Patrick},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Piezoelectricity; quasi-static approximation; ultrasonic sensors; piezoelectricity; quasi-state approximation; ultrasonic sensor},
language = {eng},
month = {2},
number = {4},
pages = {875-909},
publisher = {EDP Sciences},
title = {Mathematical and numerical modelling of piezoelectric sensors},
url = {http://eudml.org/doc/277852},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Imperiale, Sebastien
AU - Joly, Patrick
TI - Mathematical and numerical modelling of piezoelectric sensors
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/2//
PB - EDP Sciences
VL - 46
IS - 4
SP - 875
EP - 909
AB - 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.
LA - eng
KW - Piezoelectricity; quasi-static approximation; ultrasonic sensors; piezoelectricity; quasi-state approximation; ultrasonic sensor
UR - http://eudml.org/doc/277852
ER -

References

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