Vibration Characteristics And Experimental Study Of Non-Smooth Double Pendulum Under Parametric Excitation

The double pendulum model is a common vibration system with rich dynamic behavior.As a typical case of strong nonlinear problem,collision vibration is widely used in various fields of practical engineering.Based on the characteristics of the movement of the legs during the robot walking process,this paper constructs a non-smooth double pendulum experimental device,which combines the double pendulum and collision problems to study the non-smooth dynamic behavior of the double pendulum.In this paper,the two-pendulum motion model under parametric excitation is designed.The motion differential equation of the system is established by Lagrange method,and its dimensionless treatment is 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 is obtained by theoretical deduction.The mass ratio of two rods can be determined according to the length ratio.On this basis,the differential equations are linearized and decoupled into two Matthew equations by modal analysis.Finally,the stability interval of the system is determined by Lindstede-Poincare perturbation method(L-P),and the correctness of the results is verified by numerical simulation with MATLAB.According to the existing laboratory conditions,the experimental scheme is designed for the parameter-excited double pendulum system.Furthermore the specific parameters of the experimental device is obtained through continuous optimization,and the experimental device is processed.After the experimental system is designed,the experimental studies of collision-free,collision of the upper left block and collision of the left lower block are carried out.Select the different excitation amplitudes,the manual frequency sweeps of excitation frequency are carried out.The experimental results are analyzed from four aspects: time history diagram,phase diagram,Poincaré section diagram and spectrum diagram.The experimental results and simulation results are mutually verified,and the stability interval of the system under different excitation amplitudes of different operating conditions is obtained.It is found that the collision changes the frequency range of the periodic motion of the system.If the excitation amplitude remains the same,the frequency range of the system can be lengthened by selecting the appropriate collision point.The left lower block is more stable in a wider excitation frequency range than the left upper block.The research of this paper has laid a certain experimental theoretical foundation for the stable design of robot and mechanical arm system.