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Dynamic vehicle–bridge interaction (VBI) plays a crucial role in the train-induced vibrations of a railway bridge for its coupling effects may reduce the bridge response and down-shift the resonant speed. The commonly used nominal theoretical resonant speed ($=f_{b}D)$ of a typical railway bridge, however, is only related to the bridge frequency ($f_b)$ and car length ($D)$, but it neglects the VBI effects of the moving trains. Such a shifted resonance phenomenon would become significant for a bridge under two trains passing by each other. This study develops a method using an equivalent modal mass to be added onto the bridge to account for the frequency shift due to the presence of multiple train cars for estimation of the shifted resonant speed. The numerical study demonstrates that the proposed method can predict the shifted resonant speed and explain the shifted-resonance phenomenon of railway bridges under train passages.

Train-induced resonance of a railway bridge occurs when the train speed coincides with the primary resonance speed ($v_{\mathrm{\text{br}}}$) of the bridge, from which we can determine the sub-resonance speed as ($v_{\mathrm{\text{br}}}∕n{|}_{n=2,3}$). The primary resonance speed of a short bridge is generally much higher than the operation speeds of current high-speed trains but the corresponding sub-resonance speeds probably lie in the operation speed range. Such a resonance scenario can be observed from the vibration of a double-track bridge subjected to an eccentrically moving train, in which the deck vibration is combined by the vertical-flexural and torsional vibration modes of the bridge. Once the two modal sub-resonance speeds coincide with each other, a double sub-resonance will be developed on the bridge. In this study, an iteration-based train–bridge interaction finite element procedure will be presented to demonstrate the double resonance phenomenon. As expected, the double resonance may bring about a dramatic amplification on deck vibration. Such an excessive vibration is harmful to ballast stability and track maintenance of railway bridges.

Due to the rapid development of computer science, software, and biomedical engineering, many clinical diagnosis instruments and control system improved accordingly. The minimization and practicality of sensors, as well as the efficiency and stability of computers make simulation control system in medical instruments become the most important part of developing items. The relevant subject of course, virtual biomedical instrumentations (VBI), which combined with computer science, electrical engineering, and medical science, has become a major developing course in biomedical education.

Cross-disciplinary research needs experts in different areas and most cross-disciplinary schools cannot afford it. So it requires integration and cooperation between schools. To address this issue, a graduated course has been designed to provide an opportunity for all professions in each field to discuss and share their resources on an e-learning platform.

With the progress of the project, VBI course integrates biomedical education resources from north to south colleges to reduce the request of manpower for cross-disciplinary course of biomedical. In addition, VBI courses initiate the cooperation between academic community and industry.