In this work, the dynamic response of a cable-stayed bridge that consists of a simply supported four-cable-stayed deck beam and two rigid towers, subjected to a moving vehicle load, is studied. The vehicle is modeled as a mass-spring-damper system moving at a constant velocity, which is assumed to keep contact with the deck beam at all times. Convective velocity and acceleration terms associated with the moving vehicle as it traverses along the vibrating deck beam are taken into consideration, as well as geometric nonlinearities of stay cables. The nonlinear response of the cable-stayed bridge is obtained by solving nonlinear and linear partial differential equations which 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 relations of exact mode shapes of the linearized undamped cable-stayed bridge model are employed to convert the coupled nonlinear partial differential equations of the original nonlinear cable-stayed bridge model to a set of ordinary differential equations by using the Galerkin method. The dynamic response of the cable-stayed bridge is calculated using the Runge-Kutta-Fehlberg method in MATLAB. Convergence of the dynamic response from the Galerkin method is investigated for two cases in which the velocities or masses of the moving vehicle are different. Results show that an accurate calculation of the dynamic response of the cable-stayed bridge needs use of a large number of modes of the linearized undamped cable-stayed bridge model, and needs many more modes for the deck beam than stay cables. Moreover, effects of the velocity and mass of the moving vehicle and the convective terms on the dynamic response of the cable-stayed bridge are studied with convergent Galerkin truncation.
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