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The variation of the instantaneous frequencies of bridges under moving vehicles is a problem not well studied in the literature. A theoretical framework is presented for the problem, considering the variation in frequencies for both the bridge and moving vehicle. First, the equations of motion are written for the two sub-systems. By solving the eigenvalue problem, analytical solutions in closed-form are derived from the frequencies of the vehicle and bridge that are coupled with each other. Based on this, the variation pattern, range, and dominating factors involved are studied, along with the special cases of moving mass and moving load. The results reveal that, if a moving vehicle is to be used as a tool for measuring the bridge frequencies or for detecting the bridge damages, the frequency variation caused by moving vehicles should be taken into account. Such an effect will be crucial when the vehicle mass is not negligible compared with the bridge mass or when the resonance condition is approached.

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