双足模型可模拟人的周期步行问题。基于ISO 5982模型与双足模型,建立了新型双足步行模型。采用Lagrange方程描述步行过程中的运动方程,确定了系统的质量矩阵、刚度矩阵、阻尼矩阵和荷载向量。研究了人体步行的力学特性及能量变化过程,分析了腿刚度、冲击角和步行速度等参数对地面反力的影响。结果表明:新型双足模型能够模拟包括双足和单足支撑阶段完整连续的步行过程;连续平稳步行中的总能量恒定,各能量随步行过程在重力势能、弹性势能和动能之间转化;腿刚度、冲击角和步行速度对步行特性有较大影响,但腿刚度对步行周期和步长的影响较小。
Abstract
It has previously been shown that a bipedal model can be employed to simulate periodic human walking. Based on the model in ISO 5982 and bipedal model, a new bipedal model is introduced. The dynamic equation of human walking is established by means of the Lagrange equation. The mass, damping, stiffness matrices, and the force vector of the system were defined from these equations. Walking characteristics and energy change is studied. And the effects of stiffness, impact angle and walking speed are investigated. The results show that the new bipedal model can reproduce periodic walking cycle that consists of the single and double support phases. The total energy of the model is constant, which convert between the gravitational potential energy, kinetic energy and elastic potential energy. Variations in the leg stiffness, attack angle and walking speed had a substantial effect on the walking characteristics, and increase in leg stiffness had a small effect on the period and step length.
关键词
生物力学 /
双足模型 /
步行荷载 /
动力方程 /
数值模拟
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Key words
biomechanics /
bipedal model /
walking loads /
dynamic equation /
numerical simulation
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参考文献
[1] Woumuth B, Surteees J. Crowd-related failure of bridges [J]. Civil Engineering, Proceedings of ICE, 2003, 156: 116-123.
[2] 陈政清,华旭刚. 人行桥的振动与动力设计 [M]. 北京: 人民交通出版社,2009.
Chen Zhengqing, Hua Xugang. Vibration and Dynamic Design of Footbridges [M]. Beijing: China Communications Press, 2009.
[3] Dallard P, Fitzpatrick A J, Flint A. R, et al. The London Millennium Footbridge [J]. The Structural Engineer, 2001, 79(22): 17-23.
[4] 陈建英,方之楚. 人—结构相互作用动力学建模研究[J]. 振动与冲击,2007, 26(6): 10-13.
Chen Jianying, Fang Zhichu. Study on modeling of human occupants-structure dynamic interaction [J]. Journal of vibration and shock, 2007, 26(6): 10-13.
[5] 秦敬伟,杨庆山,杨娜. 人体-结构系统静态耦合的模态参数 [J]. 振动与冲击,2012, 31(15): 150-157.
Qin Jingwei, Yang Qingshan, Yang Na. Modal parameters of human body-structure static interaction systems [J]. Journal of vibration and shock, 2012, 31(15): 150-157.
[6] Mansfield N J and Griffin M J. Non-linearities in apparent mass and transmissibility during exposure to whole-body vertical vibration [J]. Journal of Biomechanics, 2000, 33(8): 933–941.
[7] Matsumoto Y and Griffin M J. Mathematical models for the apparent masses of standing subjects exposed to vertical whole-body vibration [J]. Journal of Sound and Vibration, 2003, 260(3): 431-451.
[8] Sachse R, Pavic A and Reynolds P. Human-structure dynamic interaction in civil engineering dynamics: a literature review [J]. The Shock and Vibration Digest, 2003, 35(1): 3-18.
[9] Kim S H, Cho K I, Choi M S, et al. Development of human body model for the dynamic analysis of footbridges under pedestrian induced excitation [J]. Steel Structures, 2008, 8(4): 333-345.
[10] ISO 5982. Vibration and shock-Mechanical driving point impedance of the human body [S]. Geneva, Switzerland: ISO, 1981.
[11] Geyer H, Seyfarth A and Blickhan R. Compliant leg behaviour explains basic dynamics of walking and running [J]. Proceedings of the royal society B: Biological Sciences, 2006, 273(1603): 2861-2867.
[12] Whittington B R, Thelen D G. A simple mass-spring model with roller feet can induce the ground reactions observed in human walking [J]. Journal of Biomechanical Engineering, 2009, 131(1): 011013—1-8.
[13] Kim S, Park S. Leg stiffness increases with speed to modulate gait frequency and propulsion energy [J]. Journal of Biomechanics, 2011, 44(7): 1253-1258.
[14] Qin J W, Law S S, Yang Q S, et al. A pedestrian–bridge dynamic interaction, including human participation [J]. Journal of Sound and Vibration, 2013, 332(4): 1107-1124.
[15] Seyfarth A, Geyer H, Gunther M, et al. A movement criterion for running [J]. Journal of Biomechanics, 2002, 35(5): 649-655.
[16] Bachmann H, Ammann W. Vibration in structures-induced by man and machines [M]. Structural Engineering Documents No.3a. Zurich: International Association for Bridge and Structural Engineering (IABSE), 1987.
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脚注
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