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

• Authors: M. Wiciak
• Languages of publication: 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.

Keywords

EN

43.40.At; 43.40.Vn

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2012
• Volume: 121
• Issue: 1A
• Pages: A-142-A-147

Dates

published

2012-01

Contributors

author

M. Wiciak

• Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Cracow, Poland

References

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• [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)

Identifiers

DOI

10.12693/APhysPolA.121.A-142