An Analytical Study on Dynamic Response of Multiple Simply Supported Beam System Subjected to Moving Loads

Abstract

Based on Euler–Bernoulli beam theory, first, partial differential equations were established for the vibration of multiple simply supported beams subjected to moving loads. Then, integral transforms were conducted on the spatial displacement coordinate and time in the partial differential equations, and the frequency-domain response of multiple simply supported beams subjected to moving loads was obtained. Next, by conducting the corresponding inverse transforms on the displacement frequency-domain responses of multiple simply supported beams, the spatial displacement time-domain responses were obtained. Finally, to validate the analytical method reported in this paper, the dynamic response of a typical double simply supported rail-bridge beam system of high-speed railway in China subjected to a moving load was carried out. The results show that the analytical solution proposed in this paper is consistent with the results obtained from a finite element analysis, validating and rationalizing the analytical solution. Moreover, the system parameters were analyzed for the dynamic response of double simply supported rail-bridge beam system in high-speed railway subjected to a moving load with different speeds; the conclusions can be beneficial for engineering practice.

Dynamic Response Analysis of a Simply Supported Double-Beam System under Successive Moving Loads

“…The vertical vibration of the double-beam system shown in Figure 1 is governed by the two coupled partial differential equations [35]: The vertical vibration of the double-beam system shown in Figure 1 is governed by the two coupled partial differential equations [35]:…”

“…To solve the above vibration partial differential equations, the first step is to perform a finite sin-Fourier transform for space coordinate x; for 0 ≤ x ≤ l, the finite sin-Fourier transform can be defined as follows [35]:…”

Evaluating the Dynamic Response of the Bridge‐Vehicle System considering Random Road Roughness Based on the Moment Method

“…e bridge-vehicle interaction (BVI) vibration caused by vehicles passing through the bridge will have a direct impact on the working state and service life of the bridge. It is an important design measure to evaluate the structural design parameters such as the stability and safety of vehicles running on the bridge [1,2]. e main causes of the BVI vibration are vehicle dynamic characteristics, road roughness, vehicle braking, vehicle speed, dynamic characteristics of the bridge's structure, bridgehead overlap, bridge deck local potholes, vehicle driving position, etc.…”

Earthquake Influence on the Rail Irregularity on High-Speed Railway Bridge

“…Moreover, with the needs of increasing the train speed, high-speed railways (HSRs) with the ballastless track, as shown in Figure 2, have been widely constructed in the world [17,18]. Analytical studies pointed out critical speed existed for the train passing through HSR bridges [19,20]. Many types of research studied the influence of irregularity on the train-bridge coupling vibration on an HSR line.…”