Coexisting Regimes in Hysteresis Zone in Platform-Vibrator with Shock

Abstract

Molding processes are among the most important in the manufacture of reinforced concrete structures. Vibration and shock-vibration technologies for concrete mixtures compaction and concrete products molding have the greatest distribution in the construction industry. Therefore, the issues of optimizing vibration modes, correct choice of vibration equipment do not lose their relevance. The article discusses the dynamical behavior of a shock-vibrational low-frequency resonant machine. Its mathematical model corresponds to a two-body 2-DOF vibro-impact system with a soft impact, which is simulated by a nonlinear interactive contact force in accordance with Hertz’s quasi-static contact theory. Changing the control parameters can, on the one hand, improve the compaction process, but, on the other hand, lead to unwanted vibrational modes. The article discusses such control parameters as the exciting frequency, the technological mass of the mold with concrete, and the stiffness parameters of elastic elements. Decreasing the exciting frequency, the mold mass, the vibro-isolating spring stiffness and increasing the Young’s modulus of elasticity of the rubber gasket provide an increase in impact acceleration, which improves the compaction process. However, with such changes in the parameters, coexisting regimes arise, many of which are undesirable. These are modes with a large periodicity and several impacts per cycle, chaotic modes, and transient chaos. The regime diagnostics is performed by traditional numerical means, namely, by constructing time series, phase trajectories, Poincaré maps, Fourier spectra, and the largest Lyapunov exponent. We hope that this analysis can help avoid unwanted platform-vibrator behaviour during design and operation. The presentation is accompanied by many graphs and a table.