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2012 | 121 | 1A | A-142-A-147
Article title

Analytical Solution of the Problem of Vibration of Plates with Piezoelectric Actuators with Arbitrary Shape in Distribution Formulation

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EN
Abstracts
EN
This paper is concerned with mathematical aspects of modelling vibration of a plate with piezoelectric actuators. Particularly, a thin Kirchhoff-Love plate with arbitrary shaped actuators (e.g. triangles, parallelograms, discs) is considered. The moments that act upon a structure and are induced by piezoelectric actuators, are described by the generalized tensor product of a distribution and distribution-valued function. Finally, the formula for the solution of the Cauchy problem in the class of absolutely continuous tempered distribution-valued functions is derived.
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EN
Publisher

Year
Volume
121
Issue
1A
Pages
A-142-A-147
Physical description
Dates
published
2012-01
Contributors
author
  • Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Cracow, Poland
References
  • [1] E.K. Dimitriadis, C.R. Fuller, C.A. Rogers, J. Vib. Acoust. 113, 100 (1991)
  • [2] P. Gardonio, S.J. Elliott, J. Acoust. Soc. Am. 117, 2046 (2005)
  • [3] E.M. Sekouri, Y.R. Hu, A.D. Ngo, Mechatronics 14, 1007 (2004)
  • [4] J.M. Sullivan, J.E. Hubbard, Jr., S.E. Burke, J. Acoust. Soc. Am. 99, 2965 (1996)
  • [5] L.S. Sobolev, Mat. Sb. 1, 39 (1936) (in French)
  • [6] L. Schwartz, Théorie des distributions, Hermann, Paris 1951
  • [7] W. Rudin, Functional Analysis, McGraw-Hill, New York 1973
  • [8] H.G. Embacher, G. Grubl, M. Oberguggenberger, Z. Analysis Anwendungen 11, 437 (1992)
  • [9] M. Wiciak, Univ. Iagel. Acta Math. 42, 31 (2004)
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.bwnjournal-article-appv121n1a30kz
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