Volume 43 Issue 6
Jun.  2022
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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
Citation: 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

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

doi: 10.21656/1000-0887.420177
  • Received Date: 2021-06-28
  • Rev Recd Date: 2021-08-13
  • Available Online: 2022-05-16
  • Publish Date: 2022-06-30
  • 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.

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