A moving load amplitude spectrum for analyzing the resonance and vibration cancellation of simply supported bridges under moving loads

A novel method for analyzing the resonance and vibration cancellation of simply supported bridges in the frequency domain by using moving load amplitude spectrum (MLAS) is presented in this paper. Firstly, the Fourier transform for the motion equation of simply supported bridge under equidistant moving loads is carried out derive the bridge's moving load spectrum and displacement response spectrum. The MLAS, which can be obtained by taking the modulus of the moving load spectrum, is related to the moving loads and the vibration modes of the bridge. Surprisingly, the MLAS can effectively reflect the displacement amplitude laws of the bridge free vibration excited by the moving loads. Then, the resonance and vibration cancellation of the simply supported bridge under equidistant moving loads are analyzed respectively based on the proposed MLAS. It is noted that the corresponding resonance speed obtained by the proposed MLAS is a supplement to the traditional resonance speed which sometimes doesn't cause the maximum displacement response of simply supported bridges. What's more, the vibration cancellation of the simply supported bridge under equidistant moving loads is divided into two types in this paper.The corresponding cancellation speeds v(c1-can) and v(c2-can) are determined simply by the proposed MLAS in the frequency domain. The time-domain analysis in many references only gives the cancellation speeds v(c1-can) but not the cancellation speeds v(c2-can) presented in this paper. Therefore, the cancellation speeds v(c1-can) and v(c2-can) presented in this paper can provide a more comprehensive understanding the influence factors of vibration cancellation. Finally, the relevant theoretical researches on the proposed MLAS are validated with several examples by comparing the results of the time-domain analysis.