车-桥耦合系统频率与阻尼比演化理论研究

THEORETICAL ANALYSIS OF FREQUENCY AND DAMPING RATIO EVOLUTION OF VEHICLE-BRIDGE INTERACTION SYSTEMS

  • 摘要: 为揭示车-桥耦合效应对系统模态频率与阻尼比时变特性的影响,本文建立了系统频率与阻尼比演化理论。构建了车-桥耦合系统模态频率与阻尼比演化解析式,分析了模态频率和阻尼比随车桥频率比、车桥质量比、车桥阻尼比和车桥相对位置的变化规律;探究了车-桥耦合系统趋于共振时,车桥频率比和车桥阻尼比对系统模态频率和阻尼比变化的影响机理;分析了系统模态频率与阻尼比极值点数量和位置随车桥相对位置的变化规律,探讨了车桥频率比、车桥质量比和车桥阻尼比的影响。研究结果表明:解析解与有限元结果吻合良好,验证了本文系统模态频率与阻尼比演化分析理论的可靠性;车桥系统趋于共振时,频率与阻尼比的变化规律存在显著差异;针对简支梁体系,桥梁频率在车辆位于跨中时取得极值,且其变化趋势由车桥频率比主导;当车桥质量比远小于1、车桥阻尼比大于1,此时桥梁阻尼比在车辆位于跨中时达到最大值,即车辆对桥梁阻尼效应有强化作用;随着车桥质量比增大,跨中的桥梁阻尼比由最大值可转为极小值,极大值位置则对称分布于桥梁两侧。

     

    Abstract: A theoretical framework is developed to describe the evolution of modal frequencies and damping ratios of vehicle–bridge interaction (VBI) systems. Analytical solutions are derived and validated against finite element results, with the effects of the vehicle–bridge frequency ratio, mass ratio, damping ratio, and relative vehicle position systematically examined, along with the governing mechanisms near resonance. Key findings include: the frequency and damping ratio exhibit markedly different variation patterns near resonance; for a simply supported beam, the bridge frequency attains its extreme value at midspan, governed primarily by the vehicle–bridge frequency ratio; when the mass ratio is much less than unity and the damping ratio exceeds unity, the bridge damping ratio reaches its maximum at midspan, indicating a vehicle-induced damping enhancement effect; as the mass ratio increases, this maximum damping ratio can be reduced to the minimum, with the maximum values shifting symmetrically to both sides of the bridge.

     

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