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| Periodically stable vibration of homogeneous rod-shaped double pendulum under parametric excitation |
| ZHANG Hongqiao1， TIAN Ruilan2， CHEN Enli1,2， GUO Xiuying2 |
1.School of Mechanical Engieering，Shijiazhuang Tiedao University，Shijiazhuang050043,China;
2.State Key Laboratory of Mechanical Behavior in Transfertation Engineering Structure and System Safety，Shijiazhuang Tiedao University，Shijiazhuang050043,China |
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Abstract 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.
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Received: 05 December 2018
Published: 15 August 2020
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