On the dissipative effect of a magnetic field in a Mindlin-Timoshenko plate model

In this paper we are concerned with a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. The magnetic field that permeates the plate consists of a non-stationary part and a uniform (constant) part. When the uniform magnetic field i...

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Bibliographic Details
Published in:	Zeitschrift für angewandte Mathematik und Physik Vol. 63; no. 6; pp. 1047 - 1065
Main Author:	Grobbelaar-Van Dalsen, Marié
Format:	Journal Article
Language:	English
Published:	Basel SP Birkhäuser Verlag Basel 01-12-2012
Subjects:	Engineering Mathematical Methods in Physics Theoretical and Applied Mechanics Mindlin-Timoshenko plate Magnetic field Primary 74K10 Secondary 93B15 Dissipation
Online Access:	Get full text
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Summary:	In this paper we are concerned with a linear model for the magnetoelastic interactions in a two-dimensional electrically conducting Mindlin-Timoshenko plate. The magnetic field that permeates the plate consists of a non-stationary part and a uniform (constant) part. When the uniform magnetic field is aligned with the mid-plane of the plate, a strongly interactive system emerges with direct coupling between the elastic field and the magnetic field occurring in all the equations of the system. The unique solvability of the model is established within the framework of semigroup theory. Spectral analysis methods are used to show strong asymptotic stability and determine the polynomial decay rate of weak solutions.
ISSN:	0044-2275 1420-9039
DOI:	10.1007/s00033-012-0206-z