Nonlinear Free Vibrations of Suspension Bridges: Theory

Abstract

A general theory and analysis of the nonlinear free coupled vertical‐torsional vibrations of suspension bridges with horizontal decks are presented. Approximate solutions are developed by using the method of multiple scales via a perturbation technique. The amplitude‐frequency relationships for any single set of coupled vertical‐torsional modes are presented for three cases: (1) When the large‐amplitude vertical vibration is dominating the motion; (2) when large‐amplitude torsional vibration is dominating; and (3) when one of the linear natural frequencies of vertical vibration is equal to, or approximately equal to, another linear natural frequency of torsional vibration, and the two modes are strongly coupled; this contrasts with the linear solution, which predicts that the two modes are uncoupled.