Non-Smooth Grazing Dynamics for Cantilever Beams With Bilateral Elastic Constraints

SHI Meijiao; XU Huidong; ZHANG Jianwen

doi:10.21656/1000-0887.420177

Volume 43 Issue 6

Jun. 2022

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Article Navigation > Applied Mathematics and Mechanics > 2022 > 43(6): 619-630

SHI Meijiao, XU Huidong, ZHANG Jianwen. Non-Smooth Grazing Dynamics for Cantilever Beams With Bilateral Elastic Constraints[J]. Applied Mathematics and Mechanics, 2022, 43(6): 619-630. doi: 10.21656/1000-0887.420177

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Non-Smooth Grazing Dynamics for Cantilever Beams With Bilateral Elastic Constraints

doi: 10.21656/1000-0887.420177

1.
College of Mathematics, Taiyuan University of Technology, Taiyuan 030024, P.R.China
2.
College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan 030024, P.R.China

Received Date: 2021-06-28
Rev Recd Date: 2021-08-13

Available Online: 2022-05-16

Publish Date: 2022-06-30

Abstract

Abstract

The grazing-induced non-smooth dynamical behaviors of single-degree-of-freedom cantilever beam systems with bilateral elastic constraints were studied. Firstly, based on the dynamical equations for the cantilever beam under elastic impacts and the definition of grazing points, the existence condition for the bilateral grazing periodic motion was analyzed. Secondly, the zero-velocity Poincaré section was selected to derive the high-order discontinuous mapping with parameters near bilateral grazing orbits. Then a new composite piecewise normal form mapping was established through combination of the smooth flow mapping and the high-order discontinuous mapping. Finally, the validity of the high-order mapping was verified through comparison of the bifurcation diagram of the low-order mapping with that of the high-order mapping, and the grazing dynamics of the cantilever beam under elastic impacts were further revealed through numerical simulation.
- cantilever beam,
- bilateral elastic constraint,
- discontinuous mapping,
- grazing non-smooth bifurcation

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References(12)

References

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