中文摘要：

为了快速地得到颗粒碰撞后的运动状态，从而实现颗粒碰撞阻尼系统的整体仿真研究，建立颗粒在单个碰撞周期中的分段力学模型。该模型将颗粒的单个碰撞周期分为三个阶段，通过三个阶段的力学分析得出颗粒在关键节点的运动状态，最终得到颗粒碰撞后的反弹速度、碰撞过程中的恢复系数和能量损耗的解析表达式。随后采用有限元方法对两颗粒的弹塑性碰撞过程进行模拟，有限元分析结果与分段力学模型的结果吻合较好，证明了分段力学模型的正确性。最后应用此分段力学模型对颗粒的碰撞速度、颗粒材料参数包括屈服点、弹性模量、密度和颗粒大小对耗能效果的影响进行定量的分析计算。计算结果表明，材料的屈服点和弹性模量之比越小，碰撞耗能效果越好；同时，质量密度越大的材料，耗能效果也越好；在设计颗粒阻尼器时可以以此为原则选用碰撞伙伴的材质。以上研究结果可以用于颗粒碰撞阻尼系统的阻尼特性分析和整体仿真研究。

英文摘要：

To rapidly obtain the moving state of particle impact and simulate the particle impact damping system, a piecewise dynamic model is proposed for collision of two particles in a single period. In this model, a single impact period is divided into three stages, on the basis of which, the moving state of some key points for particles and thus the analytical expressions of velocity after impact, coefficient of restitution and energy dissipation are obtained. Finite element method （FEM） is used to simulate elastoplastic impact process of two particles, and the FEM results show good agreement with the analytical prediction, which verifies the proposed piecewise dynamic model. With the piecewise dynamic model, the influences of particle velocity before impact, particle material parameters including yield strength, elastic modulus, mass density, and particle size on energy dissipation are quantitatively analyzed. The results reveal that materials with low yield strength and high elastic modulus have better attenuation effect. In addition, materials with larger mass density also have better dissipation performance, which can be taken as a reference i n choosing the material of impact partners in impact damper design. The study can be applied to predicting the character of particle impact damping and simulate the vibroimpact damping system.