scholarly journals Analysis of harmonic vibration synchronization for a nonlinear vibrating system with hysteresis force

2019 ◽  
Vol 39 (4) ◽  
pp. 1087-1101
Author(s):  
Nan Zhang ◽  
Shiling Wu
Keyword(s):  
Nonlinear Vibration ◽  
Phase Difference ◽  
Nonlinear Dynamic ◽  
Dynamic Models ◽  
Harmonic Vibration ◽  
Vibration System ◽  
The Difference ◽  
Nonlinear Dynamic Models ◽  
The Stability ◽  
Nonlinear Vibration System

Harmonic vibration synchronization of the two excited motors is an important factor affecting the performance of the nonlinear vibration system driven by the two excited motors. From the point of view of the hysteresis force, the nonlinear dynamic models of the nonlinear vibration system driven by the two excited motors are presented for the analysis of the hysteresis force with the asymmetry. An approximate periodic solution for the nonlinear vibration system with the hysteresis force is investigated using the nonlinear models. The condition of harmonic vibration synchronization is theoretically analyzed using the rotor–rotation equations of the two excited motors in the nonlinear dynamic models and the stability condition of harmonic vibration synchronization also is theoretically analyzed using Jacobi matrix of the phase difference equation of two excited motors. Using Matlab/Simlink, harmonic vibration synchronization of the two excited motors and the stability of harmonic vibration synchronization for the nonlinear vibration system with the hysteresis force are analyzed through the selected parameters. Various synchronous processes of the nonlinear vibration system with the hysteresis force are obtained through the difference rates of the two excited motors (including the initial phase difference, the initial rotational speed difference, the difference of the motors parameters). It has been shown that the research results can provide theoretical basis for the design and research of the vibration system driven by the two-excited motors.

scholarly journals Effect of phase difference on dynamic characteristics for a synchronous vibrating system with double eccentric rotors

2019 ◽  
Vol 38 (2) ◽  
pp. 473-486 ◽  
Author(s):  
Nan Zhang
Keyword(s):  
Periodic Solutions ◽  
Phase Difference ◽  
Dynamic Characteristics ◽  
Nonlinear Dynamic ◽  
Dynamic Models ◽  
Initial Conditions ◽  
Nonlinear Phenomena ◽  
Vibrating System ◽  
The Difference ◽  
Nonlinear Dynamic Models

Phase difference is an important factor affecting the performances of the synchronous vibrating system driven by the two excited motors. The nonlinear dynamic models of the synchronous vibrating system under the action of the nonlinear elastic force are established. The periodic solutions for the synchronous vibrating system are theoretically derived using the nonlinear dynamic models. The stabilities of periodic solution for the synchronous vibrating system are theoretically analyzed using Jacobi matrix of the amplitude-frequency-characteristic equation. Using Matlab, the amplitude-frequency characteristics are analyzed through the selected parameters. The relations between the phase difference and the amplitude in the synchronous vibrating system are also investigated. Various nonlinear phenomena, such as the jump phenomenon and the multiple-valued periodic solutions, are reproduced using relation between the phase difference and the amplitude. The stable periodic solutions can be obtained by the different initial conditions, using Runge–Kutta method. The effects of the phase difference on the amplitude are presented for the changes of system parameters (including the stiffness of the soil and the damping of the soil, the mass of the eccentric block). The effects of the dynamic characteristics on the phase difference are analyzed through the difference rates of the two excited motors and the initial conditions of the system. It has been shown that the research results can provide a theoretical basis for the research of the synchronous vibrating system.

Synchronization Analysis of the Double Exciting Motors in Nonlinear Vibration System Based on Reaching Law

2011 ◽  
Vol 295-297 ◽  
pp. 2197-2200
Author(s):  
Xiao Hao Li ◽  
Jie Liu
Keyword(s):  
State Space ◽  
Nonlinear Vibration ◽  
Dynamic Model ◽  
Phase Difference ◽  
Sliding Mode ◽  
Design Feature ◽  
Vibration System ◽  
Reaching Law ◽  
Speed Difference ◽  
Nonlinear Vibration System

Based on the dynamic model of the nonlinear vibration system which driven by double exciting motors, the rotate speed difference and phase difference state space equations have been deduced. According to the design feature of the nonlinear vibration system and the vibration synchronization requirement of double exciting motors, the approach control synchronization strategy has been deduced with sliding mode reaching law. The practical examples and tests shows that the reaching law synchronization controller can effectively control the double exciting motors to realize the synchronization movement, and the synchronization controller has stronger robustness. The analysis result can provide the theoretical and test basis for the further exploitation of synchronization vibrating machine.

Analyzing Bifurcation, Stability and Chaos for a Passive Walking Biped Model with a Sole Foot

2018 ◽  
Vol 28 (09) ◽  
pp. 1850113 ◽  
Author(s):  
Maysam Fathizadeh ◽  
Sajjad Taghvaei ◽  
Hossein Mohammadi
Keyword(s):  
Dynamic Models ◽  
Chaotic Behavior ◽  
Bifurcation Diagrams ◽  
Behavior Simulation ◽  
Passive Walking ◽  
Low Energy Consumption ◽  
Nonlinear Dynamic Models ◽  
Soles Of The Feet ◽  
The Stability ◽  
Intrinsic Characteristic

Human walking is an action with low energy consumption. Passive walking models (PWMs) can present this intrinsic characteristic. Simplicity in the biped helps to decrease the energy loss of the system. On the other hand, sufficient parts should be considered to increase the similarity of the model’s behavior to the original action. In this paper, the dynamic model for passive walking biped with unidirectional fixed flat soles of the feet is presented, which consists of two inverted pendulums with L-shaped bodies. This model can capture the effects of sole foot in walking. By adding the sole foot, the number of phases of a gait increases to two. The nonlinear dynamic models for each phase and the transition rules are determined, and the stable and unstable periodic motions are calculated. The stability situations are obtained for different conditions of walking. Finally, the bifurcation diagrams are presented for studying the effects of the sole foot. Poincaré section, Lyapunov exponents, and bifurcation diagrams are used to analyze stability and chaotic behavior. Simulation results indicate that the sole foot has such a significant impression on the dynamic behavior of the system that it should be considered in the simple PWMs.

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