Models of elastic plates with piezoelectric inclusions part I: Models without homogenization

Mathematical and Computer Modelling

Volumn 26, Issue 5, 1997, Pages 79-106

  Canon, E ^a   Lenczner, M ^a  

^a UNIVERSITÉ DE FRANCHE COMTÉ   (France)

Author keywords

Electrical circuits; Piezoelectricity; Plate models; Singular perturbations

Indexed keywords

BOUNDARY CONDITIONS; ELASTICITY; ELECTRIC CURRENT CONTROL; INCLUSIONS; PERTURBATION TECHNIQUES; PIEZOELECTRICITY; STRUCTURAL ANALYSIS; VOLTAGE CONTROL;

ELASTIC PLATES;

PLATES (STRUCTURAL COMPONENTS);

EID: 0031236454     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0895-7177(97)00159-3     Document Type: Article

References (23)

1. H.T. Banks and R.C. Smith, The modelling of piezoceramics patch interactions with shells, plates and beams, Quart. Applied Math. 53, 353-387, (1995).
2. Ph. Destuynder, I. Legrain, L. Castel and N. Richard, Theorical, numerical and experimental discussion on the use of piezoelectric devices for control-structure interaction, European Journal of Mechanics. A Solids 11 (2), 181-213, (1992).
3. G.A. Maugin and D. Attou, An asymptotic theory of thin piezoelectric plates, Q. J. Mech. Appl. Math. 43 (3), 347-362, (1992).
4. H.A. Sosa, On the modelling of piezoelectric laminated structures, Mech. Res. Commun. 19 (6), 541-546, (1992).
5. th Symp., STAMM-8, Hollabrunn, Austria 1989, pp. 236-241, (1991).
6. J.S. Yang and J.D. Yu, Equations for a laminated piezoelectric plates, Arch. Mech. 45 (6), 653-664, (1993).
7. G. Anzelotti, S. Baldo and D. Percivale, Dimension reduction in variational problems, asymptotic development in Γ-convergence and thin structures in elasticity, Asymptotic Anal. 9 (1), 61-100, (1994).
8. D. Caillerie, Thin elastic and periodic plates, Math. Meth. in Applied Sciences 6, 159, (1984).
9. P.G. Ciarlet, Plates and Junctions in Elastic Multi-Structures, Série RMA, Volume 14, Masson, (1990).
10. P.G. Ciarlet and P. Destuynder, A justification of the two-dimensional plate model, Comp. Meth. Appl. Mech. Eng. 17/18, 227-258, (1979).
11. A. Raoult, Contribution à l'étude des modèles d'évolution de plaques et à l'approximation d'équation d'évolution linéaire du second ordre par des méthodes multipas, Thèse de 3ième cycle, Université Pierre et Marie Curie, Paris, (1980).
12. G. Allaire, Homogenization and two scale-convergence, SIAM J. of Math. An. 23 (26), 1482, (1992).
13. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, (1978).
14. G. Nguentseng, A general convergence result for a functional related to the theory of homogenization, SIAM J. of Math. Anal. 20 (3), 608-623, (1989).
15. E. Sanchez Palencia, Non Homogeneous Media and Vibration Theory, Lecture Notes in Physics 127, Springer-Verlag, (1980).
16. E. Canon and M. Lenczner, Modèles de plaques et d'empilement de plaques piézoélectriques, In Proceedings of the Journées Numériques de Besançon, (Edited by J.M. Crolet and M. Lenczner), Métabief, France, (1993).
17. T. Lewinski, Effective models of composite periodic plates. I. Asymptotic solution, Int. J. Solids Struct. 27 (9), 1155-1172, (1991).
18. T. Lewinski, Homogenizing stiffnesses of plates with periodic structures, Int. J. Solids Struct. 29 (3), 309-326, (1992).
19. J. Vlach and K. Singhal, Computer Methods for Circuit Analysis and Design, Van Nostrand Reinhold Company, New York, (1983).
20. Dieulesaint, Ondes Élastiques dans les Solides, Masson, (1974).
21. M. Lenczner, Modelling of a plate including a distribution of piezoelectric transducers and an electronic network and optimization of circuit parameters, In Proceeding of the Euromech 341: Smart Materials, Giens, France, (Edited by J.M. Crolet and A. Preumont), (1995); J. of Structural Control 3 (1/2), (to appear).
22. M. Lenczner, Modelling of a plate including a distribution of piezoelectric transducers and an electronic network and optimization of circuit parameters, In Proceeding of the Euromech 341: Smart Materials, Giens, France, (Edited by J.M. Crolet and A. Preumont), (1995); J. of Structural Control 3 (1/2), (to appear).
23. A.E. Green and P.M. Naghdi, On electromagnetic effects in the theory of shells and plates, Philos. Trans. Roy. Soc. London Ser. A 309 (1510), 559-610, (1983).