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

Abstract

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 cable-stayed 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.

Study of flexural wave propagation through a cable stayed beam subjected to a moving load

“…The study of the dynamic response of engineering structures under moving loads originated as early as 1905 (Kryloff, 1905) and has motivated numerous investigations. The difference between the research methods for the transient response of beams under impact loads is the difference in the methods of solving dynamic equations, which include but are not limited to Pestel and Leckie (1963) with the Matrix Method, Song et al (2016aSong et al ( , 2016b with the Eigen function expansion approach combined the Galerkin method and the Runge-Kutta-Fehlberg method, Lu and Li (2018) with the method of assumed displacement function, Zhou et al (2021) with the explicit finite element algorithm. Most of the dynamic response analysis methods (such as the above methods) are poor in directly obtaining the closed-form expression of the waveform solution of the dynamic equation.…”