基于倒摆模型的行人行走的稳定性分析

Stability Analysis of a Pedestrian’s Walking Motion Based on the Inverted Pendulum Model

摘要: 人与结构的相互作用研究中必须弄清楚人行走的动力学行为。将人体视为倒摆，通过考虑倒摆支点的简谐运动来模拟人的行走行为，本文通过对倒摆模型的稳定性分析来讨论人行走的动力学行为。分析表明倒摆支点简谐运动的水平和竖直方向的振幅之比，频率之比都对倒摆的稳定性有重要影响。数值模型证实了本文采用的理论分析方法的正确性。比较倒摆支点在不同水平和竖直频率之比下的稳定性图谱可以解释为什么正常行走的行人通常都会保持水平和竖直行走步频之比在1/2附近，由此可以印证采用倒摆模拟行人行走的可行性。在许多人和结构相互作用问题的研究中往往较难确定行人产生的激励力大小。本文的分析表明可以考虑用支点做简谐运动的倒摆来模拟行人的行走，这可以避免直接确定行人激励力的困难。这可能为人与结构相互作用研究提供了一条新的思路。

Abstract: It is essential to understand dynamics of a pedestrian’s walking motion in the study of pedestri-an-structure interaction. In this paper we investigate the stability of a pedestrian’s walking motion by using the inverted pendulum model with harmonic vibrations of the pivot point. Our theoretical research shows that not only the ratio between the lateral and vertical amplitudes, but also the ratio between the lateral and vertical frequencies of the pivot point has significant effects on the balance of the inverted pendulum. Numerical simulations are carried out to verify the correctness of theoretical analysis. Furthermore, according to comparison of stability conditions for different ratios between lateral and vertical frequencies, the reason why the ratio between the lateral and vertical frequencies is closed to 1/2 for a normal pedestrian is exposed. In many pe-destrian-structure problems it is difficult to directly determine the forces induced by pedestrians. Our research indicates that it may be a novel idea by applying the inverted pendulum model to analyze dynamic interaction between pedestrians and a structure, which avoids the difficulty of determination of forces exerted by pedestrians.