Parametric Vibration of Horizontal Cable with Sag and Deck System

This paper presents parametric vibration of a system of a horizontal cable with sag and a mass block representing a bridge deck section under axial harmonic excitation.The differential equations of the cable and the mass are established.By using the variable separation method to cable's cross displacement and taking the first two modes of the cable into account,the differential equations governing the motions of the first two generalized coordinates of the cable are derived based on Galerkin method.On the basis of the theoretical model,the theoretical solutions of the differential equations of the cable-deck system are derived with multiple-scale method.Taking Cable A20 of No.2 Nanjing Bridge over Yangtze River as an example,the vibration characteristics of the system is numerically investigated and the validity of the theoretical solutions is tested.