TY - JOUR
T1 - Bifurcation analysis of a piecewise-linear impact oscillator with drift
AU - Paez Chavez, Joseph
AU - Pavlovskaia, Ekaterina
AU - Wiercigroch, Marian
N1 - Acknowledgments The authors wish to thank Scottish Enterprise
for the financial support to this research.
Nonlinear Dynamics July 2014, Volume 77, Issue 1, pp 229–230
Erratum to: Bifurcation analysis of a piecewise-linear impact oscillator with drift
DOI: 10.1007/s11071-014-1358-5
PY - 2014/7
Y1 - 2014/7
N2 - We investigate the complex bifurcation scenarios occurring in the dynamic response of a piecewise-linear impact oscillator with drift, which is able to describe qualitatively the behaviour of impact drilling systems. This system has been extensively studied by numerical and analytical methods in the past, but its intricate bifurcation structure has largely remained unknown. For the bifurcation analysis, we use the computational package TC-HAT, a toolbox of AUTO 97 for numerical continuation and bifurcation detection of periodic orbits of non-smooth dynamical systems (Thota and Dankowicz, SIAM J Appl Dyn Syst 7(4):1283-322, 2008) The study reveals the presence of co-dimension-1 and -2 bifurcations, including fold, period-doubling, grazing, flip-grazing, fold-grazing and double grazing bifurcations of limit cycles, as well as hysteretic effects and chaotic behaviour. Special attention is given to the study of the rate of drift, and how it is affected by the control parameters.
AB - We investigate the complex bifurcation scenarios occurring in the dynamic response of a piecewise-linear impact oscillator with drift, which is able to describe qualitatively the behaviour of impact drilling systems. This system has been extensively studied by numerical and analytical methods in the past, but its intricate bifurcation structure has largely remained unknown. For the bifurcation analysis, we use the computational package TC-HAT, a toolbox of AUTO 97 for numerical continuation and bifurcation detection of periodic orbits of non-smooth dynamical systems (Thota and Dankowicz, SIAM J Appl Dyn Syst 7(4):1283-322, 2008) The study reveals the presence of co-dimension-1 and -2 bifurcations, including fold, period-doubling, grazing, flip-grazing, fold-grazing and double grazing bifurcations of limit cycles, as well as hysteretic effects and chaotic behaviour. Special attention is given to the study of the rate of drift, and how it is affected by the control parameters.
KW - drifting impact oscillator
KW - non-smooth dynamical system
KW - bifurcation analysis
KW - numerical continuation
KW - TC-HAT
KW - resonance enhanced drilling
KW - discontinuity-induced bifurcations
KW - frictional slider
KW - dynamical-systems
KW - model
KW - regimes
KW - cycles
U2 - 10.1007/s11071-014-1285-5
DO - 10.1007/s11071-014-1285-5
M3 - Article
VL - 77
SP - 213
EP - 227
JO - Nonlinear Dynamics
JF - Nonlinear Dynamics
SN - 0924-090X
IS - 1-2
ER -