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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Dynamic Behaviour of the Platform-vibrator with Soft Impact. Part 2. Interior Crisis. Crisis-Induced Intermittency

Discontinuity, Nonlinearity, and Complexity 11(1) (2022) 107--124 | DOI:10.5890/DNC.2022.03.009

V.A. Bazhenov, O.S. Pogorelova, T.G. Postnikova

Kyiv National University of Construction and Architecture, 31, Povitroflotskiy avenu, Kyiv, Ukraine

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Platform-vibrator with shock is widely used in the construction industry for compacting and molding large concrete products. Its mathematical model corresponds to a two-body 2-DOF vibro-impact system with a soft impact. A soft impact is simulated with nonlinear Hertzian contact force. When the control parameter (technological mass of mold with concrete) changes, the model exhibits interesting phenomena inherent in a nonlinear non-smooth vibro-impact system, namely: boundary and interior crises, crisis-induced intermittency, transient chaos, and a hysteresis zone. Phase trajectories with Poincar\'{e} maps, graphs of time series and contact forces, Fourier spectra, and wavelet characteristics are used in numerical investigations to determine the realized oscillatory modes. We hope this analysis can help to avoid undesirable platform-vibrator behaviour during design and operation due to inappropriate system parameters.


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