参数激励下均质杆状双摆的周期稳定振动  

Periodically stable vibration of homogeneous rod-shaped double pendulum under parametric excitation

作　　者：张红巧 田瑞兰[2] 陈恩利 郭秀英[2] ZHANG Hongqiao;TIAN Ruilan;CHEN Enli;GUO Xiuying(School of Mechanical Engieering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;State Key Laboratory of Mechanical Behavior in Transfertation Engineering Structure and System Safety,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)

机构地区：[1]石家庄铁道大学机械工程学院,石家庄050043 [2]石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室,石家庄050043

出　　处：《振动与冲击》2020年第16期231-235,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金(11872253,11602151);河北省杰出青年科学基金(A2017210177);河北省杰出青年科学基金培育项目(A2015210097);基础研究团队专项项目(311008)。

摘　　要：以机器人行走过程中双腿运动特征为基础,设计构建参数激励下均质杆状双摆运动模型。采用拉格朗日方法建立系统的运动微分方程,并对其进行无量纲化处理;针对系统两固有频率比为1∶3状态进行非线性动力学分析,通过理论推导计算得出双摆长度比和质量比关系曲线,根据杆长比即可确定两杆质量比,在此基础上,将微分方程线性化解耦为两个马修方程。采用林滋泰德—庞加莱摄动法(L-P)确定系统稳定区间,经Matlab数值模拟验证了结果的正确性。Based on the motion of both legs in the walking process of a robot,a homogeneous rod-shaped pendulum motion model under parametric was designed.The motion differential equation of the system was established by the Lagrange method,and its dimensionless treatment was carried out.Nonlinear dynamic analysis of the system with two natural frequencies ratio of 1∶3,the relationship curve between length ratio and mass ratio of double pendulum was obtained by theoretical deduction,the mass ratio of two rods could be determined according to the length ratio.On this basis,the differential equation was linearized and decoupled into two Mathieu equations.Finally,the stability interval of the system was determined by the Lindstede-Poincare perturbation method(L-P),and the correctness of the results was verified by numerical simulation with Matlab.

关 键 词：双摆 拉格朗日方法 解耦 林滋泰德—庞加莱摄动法 

分 类 号：O313[理学—一般力学与力学基础] V214[理学—力学]