Traveling Waves in a Suspension Bridge System

In this paper, we study traveling waves in a suspension bridge system governed by the coupled nonlinear wave and beam equations describing oscillations in the supporting cable and roadbed. By applying the variational method, it is proved that the suspension bridge system has at least one nontrivial traveling wave.

[1]  P. Drábek,et al.  Time-periodic oscillations in suspension bridges: existence of unique solutions , 2000 .

[2]  W. Walter,et al.  Nonlinear oscillations in a suspension bridge , 1987 .

[3]  J. Glover,et al.  Existence and stability of large scale nonlinear oscillations in suspension bridges , 1989 .

[4]  Alan C. Lazer,et al.  Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis , 1990, SIAM Rev..

[5]  L. Humphreys,et al.  Numerical mountain pass solutions of a suspension bridge equation , 1997 .

[6]  Lisa D. Humphreys,et al.  When a Mechanical Model Goes Nonlinear: Unexpected Responses to Low-Periodic Shaking , 2005, Am. Math. Mon..

[7]  Z. Ding Multiple periodic oscillations in a nonlinear suspension bridge system , 2002 .

[8]  Y. Chen,et al.  Traveling Waves in a Nonlinearly Suspended Beam: Theoretical Results and Numerical Observations , 1997 .

[9]  P. McKenna,et al.  Multiple periodic solutions for a nonlinear suspension bridge equation , 1999 .

[10]  Robert H. Scanlan,et al.  The action of flexible bridges under wind, I: Flutter theory† , 1978 .

[11]  Coupled String-Beam Equations as a Model of Suspension Bridges , 1999 .

[12]  W. Walter,et al.  Travelling waves in a suspension bridge , 1990 .

[13]  Z. Ding Nonlinear periodic oscillations in a suspension bridge system under periodic external aerodynamic forces , 2002 .

[14]  P. McKenna,et al.  The study of a nonlinear suspension bridge equation by a variational reduction method , 1993 .

[15]  Nasir Uddin Ahmed,et al.  Mathematical Analysis of Dynamic Models of Suspension Bridges , 1998, SIAM J. Appl. Math..

[16]  Z. Ding On nonlinear oscillations in a suspension bridge system , 2001 .

[17]  Stephen Johnson Encyclopedia of bridges and tunnels , 2002 .

[18]  Nonlinear Periodic Oscillations in Suspension Bridges , 2001 .

[19]  P. J. McKenna,et al.  Traveling Waves in Nonlinearly Supported Beams and Plates , 2003 .

[20]  Glenn B. Woodruff,et al.  The Failure of the Tacoma Narrows Bridge , 1941 .

[21]  Alan C. Lazer,et al.  Large scale oscillatory behaviour in loaded asymmetric systems , 1987 .