scholarly journals Merging crisis of chaotic saddle in a Duffing unilateral vibro-impact system

2011 ◽  
Vol 60 (8) ◽  
pp. 080502
Author(s):  
Feng Jin-Qian ◽  
Xu Wei
Keyword(s):  
Impact System ◽  
Chaotic Saddle

Dynamic Stability of an Impact System Connected With Rock Drilling

1969 ◽  
Vol 36 (4) ◽  
pp. 743-749 ◽  
Author(s):  
C. C. Fu
Keyword(s):  
Computer Simulation ◽  
Exact Solution ◽  
Steady State ◽  
Asymptotic Stability ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
External Excitation ◽  
Rock Drilling ◽  
Impact System ◽  
Number Of Cycles

This paper deals with asymptotic stability of an analytically derived, synchronous as well as nonsynchronous, steady-state solution of an impact system which exhibits piecewise linear characteristics connected with rock drilling. The exact solution, which assumes one impact for a given number of cycles of the external excitation, is derived, its asymptotic stability is examined, and ranges of parameters are determined for which asymptotic stability is assured. The theoretically predicted stability or instability is verified by a digital computer simulation.

Chaotic motion control of a vibro-impact system based on data-driven control method

2021 ◽  
pp. 107754632110433
Author(s):  
Xiao-juan Wei ◽  
Ning-zhou Li ◽  
Wang-cai Ding
Keyword(s):  
Motion Control ◽  
Data Model ◽  
Chaotic Motion ◽  
Control Method ◽  
Data Driven ◽  
Damping Coefficient ◽  
Input Output ◽  
Output Data ◽  
Controlled System ◽  
Impact System

For the chaotic motion control of a vibro-impact system with clearance, the parameter feedback chaos control strategy based on the data-driven control method is presented in this article. The pseudo-partial-derivative is estimated on-line by using the input/output data of the controlled system so that the compact form dynamic linearization (CFDL) data model of the controlled system can be established. And then, the chaos controller is designed based on the CFDL data model of the controlled system. And the distance between two adjacent points on the Poincaré section is used as the judgment basis to guide the controller to output a small perturbation to adjust the damping coefficient of the controlled system, so the chaotic motion can be controlled to a periodic motion by dynamically and slightly adjusting the damping coefficient of the controlled system. In this method, the design of the controller is independent of the order of the controlled system and the structure of the mathematical model. Only the input/output data of the controlled system can be used to complete the design of the controller. In the simulation experiment, the effectiveness and feasibility of the proposed control method in this article are verified by simulation results.

Response Analysis of van der Pol Vibro-Impact System with Coulomb Friction Under Gaussian White Noise

2018 ◽  
Vol 28 (13) ◽  
pp. 1830043 ◽  
Author(s):  
Meng Su ◽  
Wei Xu ◽  
Guidong Yang
Keyword(s):  
White Noise ◽  
Coulomb Friction ◽  
Gaussian White Noise ◽  
Original System ◽  
Stochastic Averaging ◽  
Response Analysis ◽  
State Variables ◽  
Van Der Pol ◽  
Impact System ◽  
The Impact

In this paper, the stationary response of a van der Pol vibro-impact system with Coulomb friction excited by Gaussian white noise is studied. The Zhuravlev nonsmooth transformation of the state variables is utilized to transform the original system to a new system without the impact term. Then, the stochastic averaging method is applied to the equivalent system to obtain the stationary probability density functions (pdfs). The accuracy of the analytical results obtained from the proposed procedure is verified by those from the Monte Carlo simulation based on the original system. Effects of different damping coefficients, restitution coefficients, amplitudes of friction and noise intensities on the response are discussed. Additionally, stochastic P-bifurcations are explored.

scholarly journals The Chaotic Saddle in the Lozi Map, Autonomous and Nonautonomous Versions

2015 ◽  
Vol 25 (13) ◽  
pp. 1550184 ◽  
Author(s):  
Carlos Lopesino ◽  
Francisco Balibrea-Iniesta ◽  
Stephen Wiggins ◽  
Ana M. Mancho
Keyword(s):  
Piecewise Linear ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
The Third ◽  
Autonomous Version ◽  
Area Preserving ◽  
Chaotic Saddle

In this paper, we prove the existence of a chaotic saddle for a piecewise-linear map of the plane, referred to as the Lozi map. We study the Lozi map in its orientation and area preserving version. First, we consider the autonomous version of the Lozi map to which we apply the Conley–Moser conditions to obtain the proof of a chaotic saddle. Then we generalize the Lozi map on a nonautonomous version and we prove that the first and the third Conley–Moser conditions are satisfied, which imply the existence of a chaotic saddle. Finally, we numerically demonstrate how the structure of this nonautonomous chaotic saddle varies as parameters are varied.

scholarly journals Stability and Manipulation of Steady Collision Conditions in Three-Vibro-Impact System

2013 ◽  
Vol 79 (800) ◽  
pp. 931-942
Author(s):  
Kazunori YAGI ◽  
Shigeo KOTAKE ◽  
Yasuyuki SUZUKI
Keyword(s):  
Impact System
Sign in / Sign up

Export Citation Format

Share Document