Non-equidistant moving load amplitude spectrum for studying resonance and cancelation phenomena of simply supported bridges under train loads

Abstract In order to analyze the impact of axle spacing on the vibration response of railway bridges, it is essential to use moving loads with non-uniform intervals, namely a non-equidistant moving load model of the train. In this paper, by incorporating this model and using the Fourier transform and modulus extraction, the corresponding moving load amplitude spectrum (MLAS) related to the moving loads and the vibration modes of bridges is deduced in the frequency domain, which can thus effectively reflect the displacement amplitude laws of the bridge free vibration. Hence, the resonance and cancelation phenomena of simply supported bridges under trains are comprehensively investigated using the presented MLAS. On the one hand, the corresponding resonance speeds obtained by the MLAS are not only related to the length of carriages, bridge frequencies, and spans, but also to the number of carriages, presenting a supplement to the traditional resonance speed, which sometimes does not cause the maximum displacement response of bridges. On the other hand, the cancelation phenomena in this paper are divided into type I and type II, and the closed-form solutions of the corresponding cancelation speeds are derived from the proposed MLAS, thus providing a more comprehensive understanding of the influencing factors of cancelation phenomena. In addition, through the MLAS comparison of different train models, it is found that the non-equidistant moving loads cannot be completely replaced by the equidistant moving loads in analyzing the resonance phenomenon of railway bridges, which is related to the ratio of the carriage length to the bridge span. The type II cancelation speeds are consistent whether moving loads are equidistant or non-equidistant. However, the type I cancelation speeds are inconsistent, and the difference is reflected in the influence of the distance between the wheel centers of each bogie and the distance between the bogie centers. These research results have been validated by time domain analyses in numerical examples. Therefore, the presented frequency domain method based on the MLAS is very valuable for comprehensively investigating the resonance and cancelation phenomena of simply supported bridges under non-equidistant moving loads.