Exponential stability of piezoelectric beams with delay and second sound

In this paper, we consider a fully‐dynamic piezoelectric beam model subjected to a magnetic effect, where the heat flux is given by Cattaneo's law. It is well known that, in the absence of delay, the dissipation produced by the heat conduction is strong enough to make the piezoelectric beams ex...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Mechanik 2024-04, Vol.104 (4), p.n/a
Main Authors: Lv, Mengxian, Wang, Junmin, Yang, Jing
Format: Article
Language:English
Subjects:
Asymptotic properties
Cantilever beams
Conduction heating
Conductive heat transfer
Heat flux
Magnetic effects
Stability
Time lag
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Summary:In this paper, we consider a fully‐dynamic piezoelectric beam model subjected to a magnetic effect, where the heat flux is given by Cattaneo's law. It is well known that, in the absence of delay, the dissipation produced by the heat conduction is strong enough to make the piezoelectric beams exponentially stable. However, time delay effects may destroy this behavior. Here, we show the existence and uniqueness of solutions through the semigroup theory. Furthermore, under a smallness condition on the delay, we prove an exponential stability result via establishing the appropriate Lyapunov functional. Finally, we numerically illustrate the asymptotic behavior of the solution.
ISSN:0044-2267
1521-4001
DOI:10.1002/zamm.202300480