TY - CHAP
T1 - Complex nonlinear response of a piecewise linear oscillator
T2 - IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments, 2010
AU - Ing, James
AU - Pavlovskaia, Ekaterina
AU - Wiercigroch, Marian
PY - 2011
Y1 - 2011
N2 - In this work an experimental piecewise linear oscillator is presented. This consists of a linear mass-spring-damper undergoing intermittent contact with a slender beam, which can be modelled as providing stiffness support only. Experimental bifurcation diagrams are presented in which a complex response is observed. Smooth bifurcations are recorded, but more typically rapid transitions between at-tractors were observed. All of the following are shown to occur: coexisting attrac-tors, basin erosion associated with grazing trajectories, pairs of unstable periodic orbits, chaotic response, loss of stability through grazing and saddle node bifurcations. All of these come into play to generate the observed experimental bifurcation scenarios. It is shown that a global analysis is important in understanding the system response, especially close to grazing conditions. Although grazing is known to cause a local change in stability, it was found that more often grazing of one orbit would cause a change in the other orbits which resulted in boundary crisis and annihilation of the attractor.
AB - In this work an experimental piecewise linear oscillator is presented. This consists of a linear mass-spring-damper undergoing intermittent contact with a slender beam, which can be modelled as providing stiffness support only. Experimental bifurcation diagrams are presented in which a complex response is observed. Smooth bifurcations are recorded, but more typically rapid transitions between at-tractors were observed. All of the following are shown to occur: coexisting attrac-tors, basin erosion associated with grazing trajectories, pairs of unstable periodic orbits, chaotic response, loss of stability through grazing and saddle node bifurcations. All of these come into play to generate the observed experimental bifurcation scenarios. It is shown that a global analysis is important in understanding the system response, especially close to grazing conditions. Although grazing is known to cause a local change in stability, it was found that more often grazing of one orbit would cause a change in the other orbits which resulted in boundary crisis and annihilation of the attractor.
UR - http://www.scopus.com/inward/record.url?scp=84861091838&partnerID=8YFLogxK
U2 - 10.1007/978-94-007-1643-8_16
DO - 10.1007/978-94-007-1643-8_16
M3 - Chapter
AN - SCOPUS:84861091838
SN - 9789400716421
VL - 30
T3 - IUTAM Bookseries
SP - 135
EP - 143
BT - IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments
A2 - Stepan, Gabor
A2 - Kovacs, Laszlo L.
A2 - Toth, Andras
PB - Springer Netherlands
Y2 - 7 June 2010 through 11 June 2010
ER -