Top

Meccanica

Published in:

01-07-2014

Asymptotic analysis of a multimaterial with a thin piezoelectric interphase

Author: Michele Serpilli

Published in: Meccanica | Issue 7/2014

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

We study the electromechanical behavior of a multimaterial constituted by a linear piezoelectric transversely isotropic plate-like body with high rigidity embedded between two generic three-dimensional piezoelectric bodies by means of the asymptotic expansion method. After defining a small real dimensionless parameter \(\varepsilon \), which will tend to zero, we characterize the limit model and the associated limit problem. We give also a mathematical justification of the model by means of a functional convergence argument. Moreover, we identify the non classical electromechanical transmission conditions between the two three-dimensional bodies.

previous article Redesign and improvement of an open circuit wind tunnel

next article 3D macro and micro-block models for limit analysis of out-of-plane loaded masonry walls with non-associative Coulomb friction

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Benveniste Y (2012) Two models of three-dimensional thin interphases with variable conductivity and their fulfillment of the reciprocal theorem. J Mech Phys Solids 60(10):1740–1752ADSCrossRefMATHMathSciNet

Bernadou M, Haenel C (1999) Numerical analysis of piezoelectric shells. In: Fortin M (ed) Plates and Shells (Quebec 1996). CRM Proceedings & Lecture Notes, vol 21. American Mathematical Society, Providence, pp 55–63

Bessoud AL, Krasucki F, Serpilli M (2008) Plate-like and shell-like inclusions with high rigidity. C R Acad Sci Paris 346:697–702CrossRefMATHMathSciNet

Bessoud AL, Krasucki F, Michaille G (2009) Multi-materials with strong interface: variational modelings. Asymptot Anal 1:1–19MathSciNet

Bessoud AL, Krasucki F, Serpilli M (2011) Asymptotic analysis of shell-like inclusions with high rigidity. J Elast 103:153–172CrossRefMATHMathSciNet

Chapelle D, Ferent A (2003) Modeling of the inclusion of a reinforcing sheet within a 3D medium. Math Models Methods Appl Sci 13:573–595CrossRefMATHMathSciNet

Ciarlet PG (1997) Mathematical elasticity: theory of plates. North-Holland, AmsterdamMATH

Fernandes A, Pouget J (2002) An accurate modelling of piezoelectric multi-layer plates. Eur J Mech A 2:629–651CrossRefMathSciNet

Geis W, Mishuris G, Sändig AM (2004) Asymptotic models for piezoelectric stack actuators with thin metal inclusions. Berichte aus dem Institut für Angewandte Analysis und Numerische, Simulation 2004/001

10.

Geymonat G, Hendili S, Krasucki F, Serpilli M, Vidrascu M (2012) Asymptotic expansions and domain decomposition. In: Proceedings of 21st international conference on domain decomposition methods, INRIA Rennes, France, 25–29 June 2012

11.

Geymonat G, Licht C, Weller T (2011) Plates made of piezoelectric materials: when are they really piezoelectric? Appl Math Model 35:165–173CrossRefMATHMathSciNet

12.

Lebon F, Rizzoni R (2010) Asymptotic analysis of a thin interface: the case involving similar rigidity. Int J Eng Sci 48:473–486CrossRefMATHMathSciNet

13.

Lebon F, Rizzoni R (2011) Asymptotic behavior of a hard thin linear interphase: an energy approach. Int J Solids Struct 48:441–449CrossRefMATH

14.

Miara B, Suàrez JS (2013) Asymptotic pyroelectricity and pyroelasticity in thermopiezoelectric plates. Asymptot Anal 81:211–250MATHMathSciNet

15.

Raoult A, Sène A (2003) Modelling of piezoelectric plates including magnetic effects. Asymptot Anal 34:1–40MATHMathSciNet

16.

Sabu N (2002) Vibrations of thin piezoelectric flexural shells: two dimensional approximation. J Elast 68:145–165CrossRefMATHMathSciNet

17.

Sène A (2001) Modelling of piezoelectric static thin plates. Asymptot Anal 25:1–20MATHMathSciNet

18.

Weller T, Licht C (2010) Asymptotic modeling of thin piezoelectric plates. Ann Solid Struct Mech 1:173–188CrossRef

19.

Weller T, Licht C (2010) Mathematical modeling of piezomagnetoelectric thin plates. Eur J Mech A 29:928–937CrossRefMathSciNet

20.

Yang J (2005) An introduction to the theory of piezoelectricity. Springer, New YorkMATH

21.

Yoshikawa S (1993) Multilayer piezoelectric actuators—structures and reliability. American Institute of Aeronautics and Astronautics, Inc., technical papers, pp 3581–3586

Title: Asymptotic analysis of a multimaterial with a thin piezoelectric interphase
Author: Michele Serpilli
Publication date: 01-07-2014
Publisher: Springer Netherlands
Published in: Meccanica / Issue 7/2014
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-014-9936-7

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 7/2014

3D macro and micro-block models for limit analysis of out-of-plane loaded masonry walls with non-associative Coulomb friction

Torsional vibration analysis of push-the-bit rotary steerable drilling system

Redesign and improvement of an open circuit wind tunnel

Nonlinear transient thermal stress analysis of thick-walled FGM cylinder with temperature-dependent material properties

Eigenproblems of two-dimensional acoustic cavities with smoothly varying boundaries by using the generalized multipole method

Forward and inverse dynamics of nonholonomic mechanical systems

Premium Partners