Abstract
The problem of the generalized Kapitsa pendulum on the stability of the vertical position of the rod under the vertical vibration of the support was studied in various settings. A vertical deformable rod with a free upper end and clamped or simply supported lower end under the action of harmonic or stationary random vibrations of the support is considered. We model the rod as a system with several degree of freedom. The conditions for stability of the upper vertical position of the pendulum are found. Both bending and longitudinal vibrations of the bar are taken into account. We found the attraction basin of the stable vertical position.
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Financial support of Russian Foundation for Basic Research is acknowledged, projects, 19-01-00208a, 20-51-S52001 MHT-a.
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Belyaev, A.K., Morozov, N.F., Tovstik, P.E., Tovstik, T.M., Tovstik, T.P. (2022). On an Attraction Basin of the Generalized Kapitsa’s Problem. In: Polyanskiy, V.A., K. Belyaev, A. (eds) Mechanics and Control of Solids and Structures. Advanced Structured Materials, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-030-93076-9_2
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DOI: https://doi.org/10.1007/978-3-030-93076-9_2
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