基于双线性滞回模型的振动冲击夯–土体耦合系统动力学演化分析

Dynamic Evolution Analysis of a Vibro-Impact Rammer-Soil Coupled System Based on a Bilinear Hysteresis Model

摘要: 振动冲击夯在运行过程中由于间隙和碰撞的作用，其与土体的相互作用表现出复杂的非光滑动力学特征。为了深入探究夯机结构参数对其工作性能的影响，本文建立了一种考虑土体非线性变形的二自由度振动冲击夯–土体耦合动力学模型。采用双线性滞回模型模拟土体的弹塑性特性，建立并利用模态叠加与解耦法求解了系统在夯实加载、夯实卸载和跳起三个阶段的动力学矩阵方程。以激励力频率为分岔参数，通过单参数分岔图、Lyapunov指数谱、Poincaré映射以及相图，系统地研究了该非光滑系统的动力学行为演化规律。研究揭示了系统从周期运动经Grazing分岔、边界碰撞分岔、鞍结分岔等进入复杂周期带与混沌带的过程，并精准捕捉了系统发生的Hopf分岔行为。最后，通过对比不同激振频率下的土体累积塑性位移，评估了系统的最佳夯实效率。

Abstract: During operation, the interaction between a vibro-impact rammer and soil exhibits complex nonsmooth dynamic characteristics due to the effects of clearance and impact. To investigate the influence of structural parameters on the operational performance of the rammer, a two-degree-of-freedom coupled dynamic model of the vibro-impact rammer-soil system is established, in which the nonlinear deformation behavior of soil is taken into account. A bilinear hysteresis model is introduced to characterize the elastoplastic behavior of the soil. The system dynamic matrix equations corresponding to the compaction loading, compaction unloading, and take-off stages are formulated and solved using modal superposition and decoupling methods. Taking the excitation frequency as the bifurcation parameter, the evolution of the dynamic behavior of the nonsmooth system is systematically investigated using single-parameter bifurcation diagrams, Lyapunov exponent spectra, Poincaré maps, and phase portraits. The results reveal the transition of the system from periodic motion to complex periodic bands and chaotic regimes through grazing bifurcations, border-collision bifurcations, and saddle-node bifurcations. In addition, Hopf bifurcation behavior occurring in the system is accurately identified. Finally, the cumulative plastic displacement of the soil under different excitation frequencies is compared to evaluate the optimal compaction efficiency of the system.