Analytical solution to Vertical Dynamic Response of Simply Supported Beam Bridge traversed by Successive Moving Loads

摘要

In this paper, vibration theory is used to deduce vertical vibration's analytical expressions of Euler- Bernoulli beam traveled by moving loads. In the analytical expression, the influences of the train's travelling speed v, the mode of vibration n, the mass m and rigidity EI of beam itself and the damping ratio ζ_n of the system are considered comprehensively. Then the calculating program is made with MATLAB to analyze the dynamic response of a bridge as an illustrative example, so as to check the correctness of the analytical solution. Then a 32 meters simply supported beam traversed by moving loads of 8 ICE3 motor cars is analyzed. The calculation results show that the analysis method in this paper can really give accurate results to the beam subjected to arbitrarily spacing loads. The analytical expressions can be applied to preliminary design of railway bridges and assessment of the expected maximum vibration levels under high-speed trains.