2022/05/25 by Clelia Marchionna, Marchionna, Clelia, Stefano Panizzi +1
Engineering · #34B30 #34C25 #35G61 #35Q74 #Classical Analysis and ODEs (math.CA) #Elasticity and Wave Propagation #FOS: Mathematics #Fluid Dynamics and Vibration Analysis #Primary: 74K30 #Secondary: 34C15 #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.2205.12884
openalex publication_date 2022/05/25 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28
We consider a conservative coupled oscillators systems which arises as a simplified model of the interaction of flexural and torsional modes of vibration along the deck of the so-called fish-bone model of suspension bridges. The elastic response of the cables is supposed to be asymptotically linear under traction, and asymptotically constant when compressed (a generalization of the slackening regime). We show that for vibrations of sufficiently large amplitude, transfer of energy from flexural modes to torsional modes may occur provided a certain condition on the parameters is satisfied. The main result is a non-trivial extension of a theorem in an our previous article to the case when the frequencies of the normal modes are no more supposed to be the same. Several numerical computations of instability diagrams for various slackening models respecting our assumptions are presented.