2018/09/25 by Denis Bonheure, Filippo Gazzola, Bonheure, Denis +3
Engineering · Mathematics · #35B10 #35B35 #35B40 #35G31 #35Q74 #37C75 #74B20 #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1809.09783
openalex publication_date 2018/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A thin and narrow rectangular plate having the two short edges hinged and the\ntwo long edges free is considered. A nonlinear nonlocal evolution equation\ndescribing the deformation of the plate is introduced: well-posedness and\nexistence of periodic solutions are proved. The natural phase space is a\nparticular second order Sobolev space that can be orthogonally split into two\nsubspaces containing, respectively, the longitudinal and the torsional\nmovements of the plate. Sufficient conditions for the stability of periodic\nsolutions and of solutions having only a longitudinal component are given. A\nstability analysis of the so-called prevailing mode is also performed. Some\nnumerical experiments show that instabilities may occur. This plate can be seen\nas a simplified and qualitative model for the deck of a suspension bridge,\nwhich does not take into account the complex interactions between all the\ncomponents of a real bridge.\n