Instability of modes in a partially hinged rectangular plate

We consider a thin and narrow rectangular plate where the two short edges are hinged whereas the two long edges are free. This plate aims to represent the deck of a bridge, either a footbridge or a suspension bridge. We study a nonlocal evolution equation modeling the deformation of the plate and we...

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Bibliographic Details
Published in:Journal of Differential Equations 2016-12, Vol.261 (11), p.6302-6340
Main Authors: Ferreira, Vanderley, Gazzola, Filippo, Moreira dos Santos, Ederson
Format: Article
Language:English
Subjects:
Asymptotic behavior
Nonlocal plate equation
Stability
Well-posedness
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Summary:We consider a thin and narrow rectangular plate where the two short edges are hinged whereas the two long edges are free. This plate aims to represent the deck of a bridge, either a footbridge or a suspension bridge. We study a nonlocal evolution equation modeling the deformation of the plate and we prove existence, uniqueness and asymptotic behavior for the solutions for all initial data in suitable functional spaces. Then we prove results on the stability/instability of simple modes motivated by a phenomenon which is visible in actual bridges and we complement these theorems with some numerical experiments.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2016.08.037