Dynamic analysis of a cable-stayed bridge subjected to a continuous sequence of moving forces

In this work, an eigenfunction expansion approach is used to study the dynamic response of a cable- stayed bridge excited by a continuous sequence of identical, equally spaced moving forces. The nonlinear dynamic response of the cable- stayed bridge is obtained by simultaneously solving nonlinear and linear partial differential equations that govern transverse and longitudinal vibrations of stay cables and transverse vibrations of segments of the deck beam, respectively, along with their boundary and matching conditions. Orthogonality conditions of exact mode shapes of the linearized cable- stayed bridge model are employed to convert the coupled nonlinear partial differential equations of the original nonlinear model to a set of ordinary differential equations by using the Galerkin method. The dynamic response of the cablestayed bridge is numerically solved. Convergence of the dynamic response from the Galerkin method is investigated. Effects of close natural frequencies, mode localization, the distance between any two neighboring forces, and geometric nonlinearities of stay cables on the forced dynamic response of the cable- stayed bridge are captured using a convergent modal truncation.