The vehicle–bridge interaction (VBI) is studied using a semi-analytical approach based on a three-mass vehicle model. As most work analyzes vehicle–bridge interaction numerically and/or analytically by treating the vehicle as a simplified lumped mass, to the best of the author’s knowledge, this work first presents the theoretical formulation of the three-mass VBI system, where a more realistic vehicle model equipped with a rigid mass and two unsprung mass-spring-damper systems is considered. By assuming the first modal vibration of beam, the semi-analytical solutions are derived, which can be served as the reference solutions for calibrating VBI analyses using different models or methods.

中文翻译：

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车桥相互作用三质量车辆模型的理论公式

使用基于三质量车辆模型的半解析方法研究车桥相互作用 (VBI)。由于大多数工作通过将车辆视为简化的集中质量来数值和/或分析地分析车桥相互作用，据作者所知，这项工作首先提出了三质量 VBI 系统的理论公式，其中更现实考虑配备刚性质量和两个非簧载质量-弹簧-阻尼器系统的车辆模型。通过假设梁的第一模态振动，导出了半解析解，可以作为使用不同模型或方法校准VBI分析的参考解。