Delay-controlled primary and stochastic resonances of the SD oscillator with stiffness nonlinearities

2018 ◽  
Vol 103 ◽  
pp. 216-235 ◽  
Author(s):  
Tao Yang ◽  
Qingjie Cao
Keyword(s):  
Sd Oscillator

scholarly journals The Effect of Fractional Damping and Time-delayed Feedback on the Stochastic Resonance of Asymmetric SD Oscillator

2021 ◽  
Author(s):  
Qiubao Wang ◽  
Hao Wu ◽  
Yuejuan Yang
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Vibration Isolation ◽  
Weak Signal Detection ◽  
Fractional Damping ◽  
System Parameters ◽  
Sd Oscillator ◽  
Delay Feedback Control ◽  
Detection Energy ◽  
Time Delayed Feedback

Abstract This paper proposes the stiffness nonlinearities and asymmetric SD (smooth and discontinuous) oscillators under time-delay feedback control with a fractional damping. With the effect of displacement and velocity feedback, the oscillator is adjusted to the desired vibration state and then the stochastic resonance (SR) is achieved. This article discusses the contribution of various system parameters and time-delay feedback to SR, especially which induced by fractional damping. It should be noted that this paper provides effective guidance for fault diagnosis and weak signal detection, energy harvesting, vibration isolation and vibration reduction.

Threshold of Multiple Stick-Slip Chaos for an Archetypal Self-Excited SD Oscillator Driven by Moving Belt Friction

2017 ◽  
Vol 27 (01) ◽  
pp. 1750009 ◽  
Author(s):  
Z. X. Li ◽  
Q. J. Cao ◽  
A. Léger
Keyword(s):  
Multiple Solutions ◽  
Coulomb Friction ◽  
Homoclinic Orbits ◽  
The Self ◽  
External Excitation ◽  
Stick Slip ◽  
Sd Oscillator ◽  
Excited System ◽  
Analytical Expressions ◽  
Natural Characteristics

In this paper, we investigate the multiple stick-slip chaotic motion of an archetypal self-excited smooth and discontinuous (SD) oscillator driven by moving belt friction, which is constructed with the SD oscillator and the classical moving belt. The friction force between the mass and the belt is modeled as a Coulomb friction for this system. The energy introduction or dissipation during the slip and stick modes in the system is analyzed. The analytical expressions of homoclinic orbits of the unperturbed SD oscillator are derived by using a special coordinate transformation without any pronominal truncation to retain the natural characteristics, which allows us to utilize the Melnikov’s method to obtain the chaotic thresholds of the self-excited SD oscillator in the presence of the damping and external excitation. Numerical simulations are carried out to demonstrate the multiple stick-slip dynamics of the system, which show the efficiency of the prediction for stick-slip chaos of the perturbed self-excited system. The results presented herein this paper demonstrate the complicated dynamics of stick-slip periodic solutions, multiple stick-slip chaotic solutions and also coexistence of multiple solutions for the perturbed self-excited SD oscillator.

scholarly journals Multiple Bifurcations of a Cylindrical Dynamical System

2016 ◽  
Vol 46 (1) ◽  
pp. 33-52
Author(s):  
Ning Han ◽  
Qingjie Cao
Keyword(s):  
Dynamical System ◽  
Limit Cycles ◽  
Homoclinic Orbits ◽  
Complex Dynamic ◽  
Pendulum System ◽  
Sd Oscillator ◽  
Bistable State ◽  
Different Types ◽  
Coupling Dynamics ◽  
Dynamic Bifurcation

Abstract This paper focuses on multiple bifurcations of a cylindrical dynamical system, which is evolved from a rotating pendulum with SD oscillator. The rotating pendulum system exhibits the coupling dynamics property of the bistable state and conventional pendulum with the ho- moclinic orbits of the first and second type. A double Andronov-Hopf bifurcation, two saddle-node bifurcations of periodic orbits and a pair of homoclinic bifurcations are detected by using analytical analysis and nu- merical calculation. It is found that the homoclinic orbits of the second type can bifurcate into a pair of rotational limit cycles, coexisting with the oscillating limit cycle. Additionally, the results obtained herein, are helpful to explore different types of limit cycles and the complex dynamic bifurcation of cylindrical dynamical system.

The codimension-two bifurcation for the recent proposed SD oscillator

2009 ◽  
Vol 59 (1-2) ◽  
pp. 19-27 ◽  
Author(s):  
Ruilan Tian ◽  
Qingjie Cao ◽  
Shaopu Yang
Keyword(s):  
Codimension Two ◽  
Sd Oscillator ◽  
Codimension Two Bifurcation

Complex dynamics of an archetypal self-excited SD oscillator driven by moving belt friction

2016 ◽  
Vol 25 (1) ◽  
pp. 010502 ◽  
Author(s):  
Zhi-Xin Li ◽  
Qing-Jie Cao ◽  
Léger Alain
Keyword(s):  
Complex Dynamics ◽  
Sd Oscillator

scholarly journals A Novel Dynamic Absorber with Variable Frequency and Damping

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Tian Wang ◽  
Ruilan Tian ◽  
Xinwei Yang ◽  
Ziwen Zhang ◽  
Xiaolong Zhang
Keyword(s):  
Coupled System ◽  
Smoothing Parameter ◽  
Current Intensity ◽  
Variable Frequency ◽  
Dynamic Vibration Absorber ◽  
Sd Oscillator ◽  
Dynamic Absorber ◽  
Control Principle ◽  
And Control ◽  
Two Degree Of Freedom

Smoothness and discontinuous (SD) oscillator is a nonlinear oscillator with the variable frequency, whose frequency can be varied with the smoothing parameter. However, how to adjust the smoothing parameter has not been solved in the actual device. In this paper, the shape memory alloy (SMA) is introduced into the SD oscillator to form the SMA-SD oscillator to adjust the smoothing parameters. Combining the SMA-SD oscillator with MRF, a nonlinear dynamic vibration absorber (DVA) with variable frequency and damping is designed. The structure and control principle of the designed DVA is studied to achieve the two variable characteristics simultaneously by adjusting the current intensity. Numerical results on a two-degree-of-freedom coupled system show that the proposed DVA can adapt to different working conditions only by adjusting the current intensity.

Harmonic and subharmonic solutions of the SD oscillator

2016 ◽  
Vol 84 (4) ◽  
pp. 2477-2486 ◽  
Author(s):  
Hebai Chen ◽  
Jianhua Xie
Keyword(s):  
Subharmonic Solutions ◽  
Sd Oscillator

THE STUDY ON THE MIDSPAN DEFLECTION OF A BEAM BRIDGE UNDER MOVING LOADS BASED ON SD OSCILLATOR

2012 ◽  
Vol 22 (05) ◽  
pp. 1250108 ◽  
Author(s):  
R. L. TIAN ◽  
X. W. YANG ◽  
Q. J. CAO ◽  
Y. W. HAN
Keyword(s):  
Moving Loads ◽  
External Excitation ◽  
Response Curves ◽  
First Order ◽  
Sd Oscillator ◽  
Driven System ◽  
Complete Elliptic Integrals ◽  
Beam Bridge ◽  
Nonlinear Behaviors ◽  
Midspan Deflection

In this paper, the midspan deflection of a beam bridge with vehicles passing through the bridge successively is investigated. The midspan deflection can be modeled as the vibration trace of smooth-and-discontinuous (SD) oscillator by considering the mode of the first order and up-and-down vibration. The nonlinear behaviors of the established model are studied and presented. KAM (Kolmogorov–Arnold–Moser) structures on the Poincaré section are constructed for the driven system without dissipation with generic KAM curve and a series of resonant points and the surrounding island chains connected by chaotic orbits. Introducing a series of complete elliptic integrals of the first and the second kind, the response curves of the system are detected, to which the effects of parameters are revealed. The relevant dynamics is depicted under external excitation exhibiting period leading to chaos. The efficiency of the bifurcation diagrams obtained in this paper is demonstrated via numerical simulations.

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