Traveling Waves in Nonlinearly Supported Beams and Plates

Abstract

The observation of the traveling waves on the Golden Gate Bridge in 1938 described in [1] motivated the research of the traveling wave solutions of the nonlinear beam equation

$$ {u_{tt}} + {u_{xxxx}} + f\left( u \right) = 0. $$

(1)

In 1988, McKenna and Walter [9] proposed a model of a suspension bridge based on (1) with f(u) = max{u, 0} - 1. They proved existence of traveling wave solutions $u(x,t) = z(x - ct) + 1$ by explicitly solving two ordinary differential equations obtained for each of the linear parts of the piecewise linear function f.