scholarly journals Control of near-grazing dynamics in impact oscillators

2005 ◽  
Vol 461 (2063) ◽  
pp. 3365-3380 ◽  
Author(s):  
Harry Dankowicz ◽  
Jenny Jerrelind
Keyword(s):  
Dynamical System ◽  
Nonlinear Oscillator ◽  
Periodic Trajectory ◽  
Piecewise Smooth ◽  
Linear Feedback ◽  
Local Analysis ◽  
Feedback Strategy ◽  
System Parameters ◽  
Impact Oscillators ◽  
Smooth Dynamical System

A method is presented for controlling the persistence of a local attractor near a grazing periodic trajectory in a piecewise smooth dynamical system in the presence of discontinuous jumps in the state associated with intersections with system discontinuities. In particular, it is shown that a discrete, linear feedback strategy may be employed to retain the existence of an attractor near the grazing trajectory, such that the deviation of the attractor from the grazing trajectory goes to zero as the system parameters approach those corresponding to grazing contact. The implementation relies on a local analysis of the near-grazing dynamics using the concept of discontinuity mappings. Numerical results are presented for a linear and a nonlinear oscillator.

scholarly journals The vibro-impact capsule system in millimetre scale: numerical optimisation and experimental verification

Meccanica ◽  
2020 ◽  
Vol 55 (10) ◽  
pp. 1885-1902
Author(s):  
Yang Liu ◽  
Joseph Páez Chávez ◽  
Jiajia Zhang ◽  
Jiyuan Tian ◽  
Bingyong Guo ◽  
...  
Keyword(s):  
Dynamical System ◽  
Mathematical Formulation ◽  
Path Following ◽  
Piecewise Smooth ◽  
Experimental Results ◽  
Scale Down ◽  
Speed Up ◽  
Small Bowel Endoscopy ◽  
Numerical Optimisation ◽  
Smooth Dynamical System

Abstract The vibro-impact capsule system has been studied extensively in the past decade because of its research challenges as a piecewise-smooth dynamical system and broad applications in engineering and healthcare technologies. This paper reports our team’s first attempt to scale down the prototype of the vibro-impact capsule to millimetre size, which is 26 mm in length and 11 mm in diameter, aiming for small-bowel endoscopy. Firstly, an existing mathematical model of the prototype and its mathematical formulation as a piecewise-smooth dynamical system are reviewed in order to carry out numerical optimisation for the prototype by means of path-following techniques. Our numerical analysis shows that the prototype can achieve a high progression speed up to 14.4 mm/s while avoiding the collision between the inner mass and the capsule which could lead to less propulsive force on the capsule so causing less discomfort on the patient. Secondly, the experimental rig and procedure for testing the prototype are introduced, and some preliminary experimental results are presented. Finally, experimental results are compared with the numerical results to validate the optimisation as well as the feasibility of the vibro-impact technique for the potential of a controllable endoscopic procedure.

scholarly journals On choosing state variables for piecewise-smooth dynamical system simulations

2018 ◽  
Vol 95 (2) ◽  
pp. 1165-1188 ◽  
Author(s):  
Jin-Song Pei ◽  
Joseph P. Wright ◽  
François Gay-Balmaz ◽  
James L. Beck ◽  
Michael D. Todd
Keyword(s):  
Dynamical System ◽  
Piecewise Smooth ◽  
State Variables ◽  
Smooth Dynamical System

Sliding in a piecewise-smooth dynamical system with a hold-on effect

2014 ◽  
Vol 378 (42) ◽  
pp. 3085-3092
Author(s):  
Elena Blokhina ◽  
Dimitri Galayko ◽  
Danièle Fournier-Prunaret ◽  
Orla Feely
Keyword(s):  
Dynamical System ◽  
Piecewise Smooth ◽  
Smooth Dynamical System

Global Analysis of the Double Impact Oscillator Dynamics

1999 ◽  
Author(s):  
František Peterka
Keyword(s):  
Global Analysis ◽  
Impact Oscillator ◽  
System Parameters ◽  
Impact Oscillators ◽  
Real Value ◽  
Simulation Results ◽  
The Impact ◽  
Impact Motion ◽  
Double Impact ◽  
Phase Motion

Abstract The double impact oscillator represents two symmetrically arranged single impact oscillators. It is the model of a forming machine, which does not spread the impact impulses into its neighbourhood. The anti-phase impact motion of this system has the identical dynamics as the single system. The in-phase motion and the influence of asymmetries of the system parameters are studied using numerical simulations. Theoretical and simulation results are verified experimentally and the real value of the restitution coefficient is determined by this method.

Sequences of Global Bifurcations and the Related Outcomes after Crisis of the Resonant Attractor in a Nonlinear Oscillator

1997 ◽  
Vol 07 (11) ◽  
pp. 2437-2457 ◽  
Author(s):  
W. Szemplińska-Stupnicka ◽  
E. Tyrkiel
Keyword(s):  
Nonlinear Oscillator ◽  
Duffing Oscillator ◽  
Nonlinear Resonance ◽  
Basins Of Attraction ◽  
Global Bifurcations ◽  
System Behavior ◽  
Coexisting Attractors ◽  
System Parameters

The problem of the system behavior after annihilation of the resonant attractor in the region of the nonlinear resonance hysteresis is considered. The sequences of global bifurcations, in connection with the associated metamorphoses of basins of attraction of coexisting attractors, are examined. The study allows one to reveal the mechanism that governs the phenomenon of the post crisis ensuing transient trajectory to settle onto one or another remote attractor. The problem is studied in detail for the twin-well potential Duffing oscillator. The boundary which splits the considered region of system parameters into two subdomains, where the outcome is unique or the two outcomes are possible, is defined.

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