基于离散单元动能转换的摇摆刚体碰撞恢复系数分析*

doi:10.16265/j.cnki.issn1003-3033.2026.03.1829

中国安全科学学报 ›› 2026, Vol. 36 ›› Issue (3): 74-80.doi: 10.16265/j.cnki.issn1003-3033.2026.03.1829

基于离散单元动能转换的摇摆刚体碰撞恢复系数分析^*

邓通发¹^,²(), 周彤¹^,², 沈铂坦¹^,², 毛秋雨¹^,²

¹ 江西理工大学土木与测绘工程学院, 江西赣州 341000
² 江西理工大学江西省环境岩土与工程灾害控制重点实验室, 江西赣州 341000

收稿日期:2025-08-20 修回日期:2025-11-10 出版日期:2026-03-31

作者简介:

邓通发 (1980—),男,江西兴国人,博士,教授,主要从事桥梁结构抗震、结构健康监测与损伤诊断、复合材料和组合结构力学行为等方面的研究。E-mail:tfdeng@jxust.edu.cn。

基金资助:
江西省千人计划项目(JXSQ2022017); 江西省自然科学基金资助(20242BAB20236); 江西省教育厅项目(GJJ2200858); 江西理工大学高层次人才项目(205200100637)

Analysis and research on collision restitution coefficient of rocking rigid body based on kinetic energy conversion of discrete elements

DENG Tongfa¹^,²(), ZHOU Tong¹^,², SHEN Botan¹^,², MAO Qiuyu¹^,²

¹ School of Civil and Surveying & Mapping Engineering, Jiangxi University of Science and Technology, Ganzhou Jiangxi 341000, China
² Jiangxi Province Key Laboratory of Environmental Geotechnical Engineering and Hazards Control, Jiangxi University of Science and Technology, Ganzhou Jiangxi 341000, China

Received:2025-08-20 Revised:2025-11-10 Published:2026-03-31

摘要/Abstract

摘要：

为解决摇摆刚体经典模型误差较大和无法求解非均质及非规则形状刚体碰撞恢复系数的问题,实现对摇摆结构更精准的动态响应预测、设计、安全评估以及振动控制,首先,在摇摆刚体质元能量转换分析基础上,离散化非均质及非规则形状刚体,分析离散单元动能转换;然后,将刚体碰撞过程分为3个阶段:第1阶段计算刚体各离散单元竖向动能被耗散后的剩余动能,第2阶段计算刚体各离散单元沿碰撞后转动角点方向动能被耗散后的剩余动能,第3阶段计算各离散单元剩余动能在内力作用下进行的转换,求解出整个过程的碰撞恢复系数;最后,借助高速数字图像相关性(DIC)测量系统开展摇摆响应测试试验,并验证离散单元动能转换方法。结果表明:该方法求得的均质矩形刚体碰撞恢复系数与试验值之间的相对误差小于3%,远小于摇摆刚体经典模型与试验值的相对误差;其求出的非均质及非规则形状刚体的碰撞恢复系数与试验值相对误差同样小于5%。采用该方法能更精准地预测摇摆结构在受到冲击后的动态响应,提供更合理的结构设计和安全评估。

关键词: 离散单元, 动能转换, 摇摆刚体, 碰撞恢复系数, 动能分布

Abstract:

In order to solve the problem that the classical model of rocking rigid body has a large error and cannot solve the collision restitution coefficient of heterogeneous and irregular rigid bodies, realize more accurate dynamic response prediction, design, safety evaluation and vibration control of rocking structure, based on the energy conversion analysis of mass element, the heterogeneous and irregular rigid bodies were discretized and the kinetic energy conversion analysis of discrete elements was carried out. The collision process of rigid body was divided into three stages. In the first stage, the residual kinetic energy of each discrete unit of rigid body was calculated after the vertical kinetic energy was dissipated. In the second stage, the residual kinetic energy of each discrete element of the rigid body was calculated after the kinetic energy had been dissipated in the direction of the rotation corner after the collision. In the third stage, the residual kinetic energy of each discrete element was converted and calculated under the action of internal force, and the collision recovery coefficient of the whole process was solved. With the help of the Digital Image Correlation (DIC) measurement system, the swing response test was carried out and the method was verified. The results show that the relative error between the collision recovery coefficient of a homogeneous rectangular rigid body obtained by this method and the experimental value is less than 3%, far less than the relative error between the classical model of a rocking rigid body and the experimental value. The relative error between the calculated collision recovery coefficients of heterogeneous and irregular rigid bodies and the experimental values is less than 5%. By this method, the dynamic response of a rocking structure after impact can be predicted more accurately, and a more reasonable structural design and safety evaluation can be provided.

Key words: discrete elements, kinetic energy conversion, rocking rigid body, collision restitution coefficient, kinetic energy distribution

中图分类号:

X915.5

邓通发, 周彤, 沈铂坦, 毛秋雨. 基于离散单元动能转换的摇摆刚体碰撞恢复系数分析^*[J]. 中国安全科学学报, 2026, 36(3): 74-80.

DENG Tongfa, ZHOU Tong, SHEN Botan, MAO Qiuyu. Analysis and research on collision restitution coefficient of rocking rigid body based on kinetic energy conversion of discrete elements[J]. China Safety Science Journal, 2026, 36(3): 74-80.

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参考文献 15

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序号	试块名称	质量m/kg	H/m	高宽比
M₁	实心木块	0.424 9	0.2	2
M₂	实心木块	0.644 3	0.3	3
M₃	实心木块	0.869 5	0.4	4
M₄	实心木块	1.097 4	0.5	5

序号	r_e	r_H	r_r	r_d
M₁	0.839 7	0.7	0.830 3	0.836 7
M₂	0.931 7	0.85	0.912 6	0.916 2
M₃	0.954 3	0.911 8	0.947 4	0.949 8
M₄	0.985 0	0.942 3	0.965 0	0.966 7

序号	试块名称	宽/m	高/m	质量/g
G₁	实心钢块	0.05	0.01	190
G₂	实心钢块	0.1	0.01	380.08

编号	构件	理论值	试验值
1	M₁+G₂	0.900 239	0.919 052
2	M₂+G₂	0.946 057	0.942 844
3	M₃+G₂	0.965 72	0.971 819
4	M₄+G₂	0.976 098	0.968 127
5	M₁+G₁(O侧)	0.857 682	0.887 779
6	M₁+G₁(O'侧)	0.913 204	0.946 139
7	M₂+G₁(O侧)	0.925 714	0.946 184
8	M₂+G₁(O'侧)	0.948 613	0.947 244
9	M₃+G₁(O侧)	0.954 417	0.948 216
10	M₃+G₁(O'侧)	0.965 848	0.969 557
11	M₄+G₁(O侧)	0.969 153	0.970 975
12	M₄+G₁(O'侧)	0.975 633	0.982 756

基于离散单元动能转换的摇摆刚体碰撞恢复系数分析^*

Analysis and research on collision restitution coefficient of rocking rigid body based on kinetic energy conversion of discrete elements

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