Parametric analysis of the nonlinear primary resonance of spatial cable suspension bridges

Abstract

A comprehensive model based on continuum theory is adopted to conduct the parametric analysis of the primary resonance of the nonlinear vibration of spatial cable suspension bridges. This model can simultaneously account for the geometric nonlinearity of both the vertical motion of the deck and the vertical-horizontal motion of the cable. Based on this model and the multiple scale method(MSM), the modulation equations of the primary resonance responses are derived for spatial cable suspension bridges. Nonlinear coefficients in the modulation equations are determined to have notable influences on the maximum response amplitude of the primary resonance of the system and the hardening or softening characteristics of the investigated vibration mode. Meanwhile, system parameters, such as the inclination angles of the main cable and hanger, the sag-to-span ratio of the cable, and the tensile stiffness ratio between the deck and cable, can notably influence the nonlinear coefficient. The dynamic properties of the system can change dramatically in the form of sudden changes in the nonlinear coefficient of the symmetric vibration of the deck and cable if the parameter is located near the singularity, which should be avoided in the design of the system. This study can provide reference for the design of the bridge structure.

Keywords

suspension bridge / spatial cable / nonlinear dynamics / multiple scale method / primary resonance