TY - JOUR
T1 - Grazing-induced bifurcations in impact oscillators with elastic and rigid constraints
AU - Jiang, Haibo
AU - Chong, Antonio S E
AU - Ueda, Yoshisuke
AU - Wiercigroch, Marian
N1 - Acknowledgements
This work is supported by: the National Natural Science Foundation of China (Grant No. 11672257 and 11402224); the Natural Science Foundation of Jiangsu Province of China (Grant Nos. BK20161314 and BK20151295); the National Secretariat of Science, Technology and Innovation of Ecuador (Grant No. 114-2012) and Escuela Superior Politécnica del Litoral of Ecuador (Grant No. 12-08-313). H. Jiang and A.S.E. Chong acknowledge the hospitality of the University of Aberdeen.
PY - 2017/7
Y1 - 2017/7
N2 - This paper investigates differences between the grazing-induced bifurcations in impact oscillators with one-sided elastic and rigid constraints by a path-following (continuation) method. The grazing bifurcations are computed and classified for both oscillators. Two-parameter smooth (period-doubling, saddle-node) and non-smooth (grazing) bifurcations are analyzed. Frequency response curves including bifurcation points are determined for different values of stiffness ratio and restitution of energy coefficient. As the stiffness ratio increases, the constraint changes from elastic to rigid and the bifurcation structure varies correspondingly. For the first time our numerical results presented in and in the current work show that for the impact oscillators with one-sided elastic constraint, the smooth (period-doubling, saddle-node) bifurcations approach the non-smooth (grazing) bifurcations as the stiffness ratio increases. However, for the impact oscillators with one-sided rigid constraint, there is no smooth bifurcations near the non-smooth (grazing) bifurcation points. Basins of attraction, computed by our newly developed Matlab-based computational suite ABESPOL , complement our study.
AB - This paper investigates differences between the grazing-induced bifurcations in impact oscillators with one-sided elastic and rigid constraints by a path-following (continuation) method. The grazing bifurcations are computed and classified for both oscillators. Two-parameter smooth (period-doubling, saddle-node) and non-smooth (grazing) bifurcations are analyzed. Frequency response curves including bifurcation points are determined for different values of stiffness ratio and restitution of energy coefficient. As the stiffness ratio increases, the constraint changes from elastic to rigid and the bifurcation structure varies correspondingly. For the first time our numerical results presented in and in the current work show that for the impact oscillators with one-sided elastic constraint, the smooth (period-doubling, saddle-node) bifurcations approach the non-smooth (grazing) bifurcations as the stiffness ratio increases. However, for the impact oscillators with one-sided rigid constraint, there is no smooth bifurcations near the non-smooth (grazing) bifurcation points. Basins of attraction, computed by our newly developed Matlab-based computational suite ABESPOL , complement our study.
KW - Discontinuity-induced bifurcations
KW - Grazing bifurcations
KW - Hysteresis
KW - Impact oscillators
KW - Non-smooth systems
KW - Path following
UR - http://www.scopus.com/inward/record.url?scp=85012881897&partnerID=8YFLogxK
U2 - 10.1016/j.ijmecsci.2017.02.001
DO - 10.1016/j.ijmecsci.2017.02.001
M3 - Article
AN - SCOPUS:85012881897
VL - 127
SP - 204
EP - 214
JO - International Journal of Mechanical Sciences
JF - International Journal of Mechanical Sciences
SN - 0020-7403
ER -