ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
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

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

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

Dynamic Behaviour of the Platform-vibrator with Soft Impact. Part 1. Dependence on Exciting Frequency

Discontinuity, Nonlinearity, and Complexity 11(4) (2022) 705--722 | DOI:10.5890/DNC.2022.12.009

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

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

Abstract

Platform-vibrators are the main molding equipment in the production of precast concrete elements. It is designed for compaction and molding of concrete products. We have created a mathematical model of a platform-vibrator with shock which is used for the manufacture of large elements. The created model corresponds to a strongly nonlinear non-smooth discontinuous 2-DOF vibro-impact system with soft impact. The simulation of soft impact with linear force and nonlinear force corresponding to qusistatic contact Hertz law is compared. The analysis of dynamic behaviour when changing the exciting frequency is performed. The zones of periodic motion, hysteresis, transient chaos, and a boundary crisis on its right border are shown. The chaoticity of the movement is confirmed by the typical form of phase trajectories, Poincar\'{e} maps, Foureir spectra, the positive sign of Lyapunov exponent, the fractal structure of Poincar\'{e} map, and the specific form of wavelet coefficients surface and its projection.

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