ANALYTICAL DYNAMICS OF A FRICTION OSCILLATOR UNDER TWO-FREQUENCY EXCITATIONS WITH FLOW BARRIERS

Guanghui Sun; Xilin Fu

doi:10.11948/20200472

2021 Volume 11 Issue 5

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Guanghui Sun, Xilin Fu. ANALYTICAL DYNAMICS OF A FRICTION OSCILLATOR UNDER TWO-FREQUENCY EXCITATIONS WITH FLOW BARRIERS[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2508-2534. doi: 10.11948/20200472

Citation:

Guanghui Sun, Xilin Fu. ANALYTICAL DYNAMICS OF A FRICTION OSCILLATOR UNDER TWO-FREQUENCY EXCITATIONS WITH FLOW BARRIERS[J]. Journal of Applied Analysis & Computation, 2021, 11(5): 2508-2534. doi: 10.11948/20200472

ANALYTICAL DYNAMICS OF A FRICTION OSCILLATOR UNDER TWO-FREQUENCY EXCITATIONS WITH FLOW BARRIERS

Guanghui Sun¹,
Xilin Fu^2, ,

1.
School of Science, Shandong Jiaotong University, Jinan, 250357, China
2.
School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

Corresponding author: Email: xilinfu@hotmail.com(X. Fu)
Fund Project: The authors were supported by National Natural Science Foundation of China(11571208), National Natural Science Foundation of China(11971275), Specialized Research Fund for the Doctoral Program of Higher Education of China(20123704110001), Shandong Provincial Natural Science Foundation(ZR2020MG001)and the Doctoral Research Initiation Fund of Shandong Jiaotong University(BS201902039)

Abstract

Abstract

In this paper, the analytical dynamics is investigated in a periodically forced friction oscillator under two-frequency excitations. The nonlinear friction force is approximated by a piecewise linear, kinetic friction model with the static friction force, $ G $-functions are defined through the dot product of the vector fields and the normal vector. By the sign of $ G $-functions, the necessary and sufficient conditions for the flow passibility and the grazing motions to the separation boundary are developed. For the examined system, the boundary possesses flow barriers caused by the static friction force. Because the flow barriers exist on the separation boundary, the singularities of the flow on such a separation boundary will be changed accordingly. Based on the critical values of flow barriers, the necessary and sufficient conditions for the onset and vanishing of the stick motions on the boundary with flow barriers are also developed. Furthermore, the periodic motions of such an oscillator are determined through the corresponding mapping structures. Illustrations of the periodic motions in such a piecewise friction model are given to verify the analytical conditions.
- Discontinuous dynamical systems /
- flow barriers /
- passable motions /
- stick motions /
- mapping structure
MSC: 34K13, 37N20

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References

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