Analytical formulations for amplifier-enhanced VBI systems

In the vehicle scanning method, using the amplifier as the tuned mass damper in the vehicle–bridge system has been shown to be able to scan the higher bridge frequencies clearly in the amplifier spectrum recently. To design a test vehicle enhanced by one or two amplifiers in practice, the analytical approach undoubtedly serves as the guideline. For this purpose, this study is aimed at deriving the analytical formulation for one amplifier-enhanced vehicle–bridge system and the semi-analytical formulation for two amplifier-enhanced vehicle–bridge system, while a miniature three-mass vehicle model is adopted. The correctness of the analytical formulations is verified by the finite element formulations through the dynamic responses of the amplifier, vehicle body, and bridge; good agreement is observed for all responses. The amplifier spectra are further provided to show the distinctly scanned bridge frequencies.