An inclined cable excited by a non-ideal massive moving deck: an asymptotic formulation

Abstract

A moving deck is an important (kinematic) excitation source for the inclined cable in cable-stayed bridges. In ideal cases, the deck motion is assumed to be harmonic oscillation and cable’s dynamic effects on the deck are neglected. As a refined version, an inclined cable excited by a massive non-ideal moving deck, i.e., the deck’s oscillation, is slowly modulated by the cable and thus not exactly harmonic is investigated in an asymptotically coupled formulation for understanding cable–deck dynamic interactions. More explicitly, by ordering the deck/cable mass ratio as a large parameter, the coupled system is reduced using asymptotic approximations and multi-scale expansions. After neglecting the reduced model’s nonlinear terms, firstly, cable–deck linear coupled modes are obtained, leading to two different kinds of linear modal dynamics, i.e., the cable-dominated one and the deck-dominated one, whose asymptotic characteristics are also revealed. Then cable’s forced nonlinear vibrations, excited by the deck’s modulated oscillation (i.e., non-ideal moving deck), are fully investigated. Nonlinear frequency responses of the cable–deck coupled system are found, and the dynamic effects on the cable’s periodic and quasi-periodic behaviors, due to cable–deck coupling (characterized by the deck/cable mass ratio), cable’s inclinations, and boundary damping, are also presented.