Nonlinear oscillations in a suspension bridge
type: Item
instance of: scholarly article
title: Nonlinear oscillations in a suspension bridge
zbMATH Open document ID: 0676.35003
DOI: 10.1007/BF00251232
published in: Archive for Rational Mechanics and Analysis
publication date: 1987-01-01T00:00:00Z
review text: This paper deals with a simplified mathematical model for a suspension bridge \[ (1)\quad u_{tt}+K_ 1u_{xxxx}+K_ 2u^+=W(x)+\epsilon f(x,t);\quad u(0,t)=u(L,t)=0,\quad u_{xx}(0,t)=u_{xx}(L,t)=0, \] where W(x) is the weight per unit length at x, and f(x,t) is an externally imposed periodic function. \textit{A. C. Lazer} and the first author [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 4, 243-274 (1987; Zbl 0633.34037)] considered (1) under the assumption that \(u(x)=W_ 0 \sin (\pi x/L).\) The paper in question deals with periodic solution of (1) in the more realistic case that \(W(x)=W_ 0\), \(0<x<L\).
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35G15
Mathematics Subject Classification ID: 35B10
zbMATH DE Number: 4107239
zbMATH Keywords: nonlinear oscillations
zbMATH Keywords: mathematical model
zbMATH Keywords: suspension bridge
zbMATH Keywords: periodic function
zbMATH Keywords: periodic solution
author: P. Joseph Mckenna
author: W. Walter
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4107239