Effect of cut-off order of nonlinear stiffness on the dynamics of a sectional suspension bridge model

Abstract

The nonlinear dynamics of a suspended bridge deck with inclined main cables and its sensitivity to the nonlinear stiffness are investigated via a 6-DoFs sectional model in this study. Four configurations with different main cable inclination angles are investigated. Two higher order numerical models are analyzed to examine the effects of higher order nonlinear stiffnesses on the dynamic properties, with one considering the linear and quadratic stiffness terms and the other includes additionally the cubic stiffness term. Incremental harmonic balance method is adopted for the nonlinear dynamic analysis, and primary resonances at the first and second modes are studied in details. Results show that the nonlinearity introduced by the inclined main cables has only very minor effects on the first primary resonance modal response. However, the cubic stiffness term shows quite strong effect on the dynamic response of the second mode. If only the linear and quadratic stiffnesses are included in the model, the frequency-response curve from the first harmonic term shows weak softening features. The system, however, performs like a hard spring when the cubic stiffness is included which is totally different from existing published results. The observations on the super-harmonic resonance at the first two modes of the system also show great differences in the behavior of the two numerical models. Results from this study suggest that the cubic nonlinear stiffness should be included for better modeling of a sectional suspension bridge model.