Grazing-induced bifurcations in impact oscillators with elastic and rigid constraints

Haibo Jiang; Antonio S E Chong; Yoshisuke Ueda; Marian Wiercigroch

doi:10.1016/j.ijmecsci.2017.02.001

Grazing-induced bifurcations in impact oscillators with elastic and rigid constraints

Haibo Jiang, Antonio S E Chong, Yoshisuke Ueda, Marian Wiercigroch^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

86 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	204-214
Number of pages	11
Journal	International Journal of Mechanical Sciences
Volume	127
Early online date	7 Feb 2017
DOIs	https://doi.org/10.1016/j.ijmecsci.2017.02.001
Publication status	Published - Jul 2017

Bibliographical note

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.

Keywords

Discontinuity-induced bifurcations
Grazing bifurcations
Hysteresis
Impact oscillators
Non-smooth systems
Path following

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title = "Grazing-induced bifurcations in impact oscillators with elastic and rigid constraints",

abstract = "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.",

keywords = "Discontinuity-induced bifurcations, Grazing bifurcations, Hysteresis, Impact oscillators, Non-smooth systems, Path following",

author = "Haibo Jiang and Chong, {Antonio S E} and Yoshisuke Ueda and Marian Wiercigroch",

note = "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 Polit{\'e}cnica del Litoral of Ecuador (Grant No. 12-08-313). H. Jiang and A.S.E. Chong acknowledge the hospitality of the University of Aberdeen.",

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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.

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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

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KW - Hysteresis

KW - Impact oscillators

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JO - International Journal of Mechanical Sciences

JF - International Journal of Mechanical Sciences

ER -

Grazing-induced bifurcations in impact oscillators with elastic and rigid constraints

Abstract

Bibliographical note

Keywords

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