Nonlinear oscillations in a suspension bridge
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 \(W(x)=W_ 0\), \(0<x<L\).
scientific article; zbMATH DE number 4107239