Finite element analysis of a Timoshenko beam traversed by a moving vehicle

Abstract

In this study the finite element formulation for the dynamics of a bridge traversed by moving vehicles is presented. The vehicle including the driver and the passenger is modelled as a half-car planner model with six degree of freedom, travelling on the bridge with constant velocity. The bridge is modelled as a uniform beam with simply supported end conditions that obeys the Timoshenko beam theory. The governing equations of motion are derived using the extended Hamilton principle and then transformed into the finite element format by using the weak-form formulation. The Newmark-β method is utilized to solve the governing equations and the results are compared with those reported in the literature. Furthermore, the maximum values of deflection for the Timoshenko and Euler-Bernoulli beams have been compared. The results illustrated that as the velocity of the vehicle increases, the difference between the maximum beam deflections in the two beam models becomes more significant. Downloaded from where ξ k , c, ρ, and ω k represent the kth mode damping ratio, the damping coefficient, the linear density, and the kth natural frequency of the beam, respectively. Accordingly, the damping ratio for the first vibration mode of the beam is equal to 3.3 per cent.

Vibration control of Timoshenko beam traversed by moving vehicle using optimized tuned mass damper

“…Initially, the equations of motion for a Timoshenko beam with the attached TMDs are obtained. The derived equations are then combined with those of the beam traversed by a moving vehicle, having been already developed by the authors, in order to obtain the governing equations of motion for the combined system (Moghaddas et al, 2009; also see Appendix A).…”

“…The finite element formulation of a Timoshenko beam traversed by a moving vehicle modeled as a half-car planar model with six degrees-of-freedom has been developed by the authors (Moghaddas et al, 2009). The equations of motion and the resulting finite element formulation are presented in Appendix A for the sake of completeness.…”

“…Simulation models for a beam under a moving vehicle vary from simple models such as 'constant moving load model', which ignores the inertia of the vehicle and the interaction between the vehicle and the bridge, to the most complete ones such as a series of 'mass-springdamper' systems which provide detailed consideration of the vehicle-bridge dynamic interaction (Au et al 2001). For a complete literature review of these models and methodologies the reader is referred to a recent paper by the authors (Moghaddas et al, 2009).…”

Vibration absorbers for simply supported beams subjected to constant moving loads

“…As for the moving vehicle, it is modeled as a dynamic system with several degrees of freedom, and when ignoring its dynamic effects, it is simply modeled as a moving mass. Moghaddas et al 1 proposed a finite element approach for the dynamic analysis of beams traversed by a moving vehicle. The latter is modeled with six degrees of freedom which include its pitch effect.…”

Vehicle strip element in the analysis of stiffened plate under realistic moving loading

“…2,11 In recent years, vehicle is usually presented with a half car model (pitch and bounce vehicle model), 12,13 or a full vehicle model. 14,15 Structure is usually modelled as a beam 5,6,16,17 or a plate [12][13][14][15] with different boundary conditions. Influence of the bridge cross section could not be observed with these simplified structure models.…”