地震与车辆作用下开裂钢筋混凝土梁刚度演化及振动分析

Stiffness evolution and vibration analysis of cracked reinforced concrete beams under seismic and vehicle loading

摘要

为揭示钢筋混凝土结构开裂对地震-车-桥耦合振动的影响机制，提出了一种考虑结构刚度时变效应的动态耦合振动分析方法。该方法融合了裂缝间钢筋-混凝土黏结滑移关系与截面非线性应变场分布模型，构建了开裂区域刚度演化计算方法，并引入刚度迭代更新算法，实现了地震-车-桥系统整体振动响应与局部刚度时变效应的动态交互。通过典型案例分析验证了所提出方法的有效性，并揭示了多因素耦合作用下结构刚度演化规律及其对振动特性的影响。研究结果表明，车辆荷载作用下钢筋混凝土梁开裂区域刚度下降显著，结构振动平衡位置发生偏移，进而使振动响应峰值增大约22%；而地震单独作用下刚度波动较小。在地震与车辆共同作用下，结构刚度进一步退化，振动响应峰值超过单一荷载作用之和，非线性特征增强；但当车辆振动响应峰值时刻与地震负峰值时刻相重合时，会出现响应抵消，使叠加响应低于车辆单独作用时的水平。

Abstract

To investigate the impact of cracking in reinforced concrete structures on the seismic-vehicle-bridge coupled vibration, a dynamic coupling analysis method considering the time-varying stiffness effect of the structure is proposed. This method integrates the bond-slip relationship between reinforcement and concrete within cracks and a nonlinear strain field distribution model of the cross-section, establishing a stiffness evolution calculation approach for cracked regions. By incorporating a stiffness iteration and update algorithm, the method enables dynamic interaction between global vibration response of the seismic-vehicle-bridge system and the local time-dependent stiffness behavior. The effectiveness of the proposed method is validated through case studies, revealing the stiffness evolution mechanism under multi-factor coupling and its influence on vibration characteristics. Results indicate that under vehicle loading, the stiffness of the cracked region in the reinforced concrete beam decreases significantly, causing a shift in the structural vibration equilibrium position and resulting in an approximate 22% increase in the peak vibration response. Under seismic loading alone, the stiffness fluctuation remains minor. However, under combined seismic and vehicle loading, further stiffness degradation occurs, resulting in vibration peaks that exceed the sum of individual loading effects and highlighting enhanced nonlinear behavior. Notably, when the vehicle-induced vibration peak coincides with the seismic negative peak, a cancellation effect may occur, reducing the combined response to be below that caused by vehicle loading alone.

关键词

钢筋混凝土梁 / 地震-车-桥耦合振动 / 混凝土裂缝 / 时变刚度 / 非线性应变分布

Key words

reinforced concrete beams / seismic-vehicle-bridge coupled vibration / concrete cracks / time-dependent stiffness / nonlinear strain distribution

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基金资助

国家自然科学基金项目(51178429)