2016
DOI: 10.1016/j.jde.2016.08.037
|View full text |Cite
|
Sign up to set email alerts
|

Instability of modes in a partially hinged rectangular plate

Abstract: Abstract. 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 … Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
1

Citation Types

2
13
0

Year Published

2018
2018
2022
2022

Publication Types

Select...
5
2

Relationship

1
6

Authors

Journals

citations
Cited by 20 publications
(15 citation statements)
references
References 20 publications
2
13
0
Order By: Relevance
“…Hence, since the equation h = Γ n (h, 0) admits a unique solution, the Leray-Schauder principle guarantees the existence of a solution h ∈ (C 0 T (R)) n of h = Γ n (h, 1). This proves the existence of a T -periodic solution u n of the finite system (13). Using similar arguments as in [7,Lemmas 19 and 20] and the expression in (15), we deduce that u n (t) H 2 * and u n t (t) L 2 are bounded in [0, T ], independently of n. The equation…”
supporting
confidence: 71%
See 3 more Smart Citations
“…Hence, since the equation h = Γ n (h, 0) admits a unique solution, the Leray-Schauder principle guarantees the existence of a solution h ∈ (C 0 T (R)) n of h = Γ n (h, 1). This proves the existence of a T -periodic solution u n of the finite system (13). Using similar arguments as in [7,Lemmas 19 and 20] and the expression in (15), we deduce that u n (t) H 2 * and u n t (t) L 2 are bounded in [0, T ], independently of n. The equation…”
supporting
confidence: 71%
“…Back to the finite dimensional Hamiltonian system (13), this proves the claimed (C 0 T (R)) n -bound (14). Hence, since the equation h = Γ n (h, 0) admits a unique solution, the Leray-Schauder principle guarantees the existence of a solution h ∈ (C 0 T (R)) n of h = Γ n (h, 1).…”
mentioning
confidence: 59%
See 2 more Smart Citations
“…Remark 2. In [7], the authors analyzed in detail how a solution of (1), initially oscillating in an almost purely longitudinal fashion, can suddenly start oscillating in a torsional way, even without the presence of external forces, that is, when h = 0. Therefore, we shall consider h = 0.…”
Section: Remarkmentioning
confidence: 99%