Volume 46, Number 4, July-August 2012
|Page(s)||875 - 909|
|Published online||03 February 2012|
Mathematical and numerical modelling of piezoelectric sensors
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.