On well-posedness for some thermo-piezoelectric coupling models

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

There is an increasing reliance on mathematical modelling to assist in the design of piezoelectric ultrasonic transducers since this provides a cost-effective and quick way to arrive at a first prototype. Given a desired operating envelope for the sensor the inverse problem of obtaining the associated design parameters within the model can be considered. It is therefore of practical interest to examine the well-posedness of such models. There is a need to extend the use of such sensors into high temperature environments and so this paper shows, for a broad class of models, the well-posedness of the magneto-electro-thermo-elastic problem. Due to its widespread use in the literature, we also show the well-posedness of the quasi-electrostatic case.
LanguageEnglish
Pages4375-4384
Number of pages12
JournalMathematical Methods in the Applied Sciences
Volume39
Issue number15
Early online date18 Feb 2016
DOIs
Publication statusPublished - 31 Oct 2016

Fingerprint

Well-posedness
Sensor
Ultrasonic transducers
Piezoelectric transducers
Sensors
Thermoelastic
Parameter Design
Inverse problems
Transducer
Mathematical Modeling
Electrostatics
Envelope
Inverse Problem
Model
Prototype
Costs
Temperature
Design
Class

Keywords

  • piezo-electric ultrasonic transducers
  • magneto-electro-thermo-elastic problem
  • quasi-electrostatic case
  • sensor
  • mathematical modelling

Cite this

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title = "On well-posedness for some thermo-piezoelectric coupling models",
abstract = "There is an increasing reliance on mathematical modelling to assist in the design of piezoelectric ultrasonic transducers since this provides a cost-effective and quick way to arrive at a first prototype. Given a desired operating envelope for the sensor the inverse problem of obtaining the associated design parameters within the model can be considered. It is therefore of practical interest to examine the well-posedness of such models. There is a need to extend the use of such sensors into high temperature environments and so this paper shows, for a broad class of models, the well-posedness of the magneto-electro-thermo-elastic problem. Due to its widespread use in the literature, we also show the well-posedness of the quasi-electrostatic case.",
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On well-posedness for some thermo-piezoelectric coupling models. / Mulholland, Anthony J.; Picard, Rainer; Trostorff, Sascha; Waurick, Marcus.

In: Mathematical Methods in the Applied Sciences, Vol. 39, No. 15, 31.10.2016, p. 4375-4384.

Research output: Contribution to journalArticle

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