Crisis-Induced Intermittency and Other Nonlinear Dynamics Phenomena in Vibro-impact System with Soft Impact

Баженов, В. Г.; Pogorelova, O. S.; Postnikova, Tetiana

doi:10.1007/978-3-030-75890-5_11

Cited by 9 publications

(10 citation statements)

References 18 publications

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“…We have studied this problem in our previous papers [23,24,25]. Now we simulate an impact with nonlinear interactive force according to contact quasistatic Hertz law [26].…”

Section: An Impact Occurs Whenmentioning

confidence: 99%

Choice of the Model for Vibro-impact Nonlinear Energy Sink

Lizunov

Pogorelova

Postnikova

2022

OMTC

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The nonlinear energy sink (NES) is defined as a single-degree-of-freedom structural element with relatively small mass and weak dissipation, attached to a primary structure via essentially nonlinear coupling. It is a passive energy dissipation device designed to rapidly absorb vibration energy (due to shock, blast, earthquakes, etc.) from a primary structure and locally dissipate it. The article contains a mini-review of the works on NESs. Design schemes for single-sided and double-sided vibro-impact NESs (SSVI and DSVI NESs) are proposed on the basis of conceptual and design NES schemes that exist in the world scientific literature. The motion equations and the impact rule are given. The quasistatic Hertz contact law is adopted as the impact rule. Various representations of the impulsive loading on the primary structure are discussed. These are excitations by initial velocities only, periodic excitation, a shock in the half-sine form, single-sided periodic impulses of a rectangular shape,wind, seismic and broadband excitation. The Tables of some numerical parameters that can be accepted for VI NES are given. Using the presented data, the authors intend to investigate both the efficiency of SSVI and DSVI NESs under different types of impulsive load, and their dynamical behavior with the changing in their parameters.

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“…We have studied this problem in our previous papers [23,24,25]. Now we simulate an impact with nonlinear interactive force according to contact quasistatic Hertz law [26].…”

Section: An Impact Occurs Whenmentioning

confidence: 99%

Choice of the Model for Vibro-impact Nonlinear Energy Sink

Lizunov

Pogorelova

Postnikova

2022

OMTC

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“…The creation of mathematical model for platform-vibrator with shock was described in detail in [14]. A detailed description of the model and its verification were made in [12,15,16]. Therefore, only a brief model description is given here in order to understand the analysis of its dynamic behavior.…”

Section: Brief Model Descriptionmentioning

confidence: 99%

“…(Or, on the contrary, it suddenly goes from the periodic movement to a chaotic one. )The lifetime of transient chaos depends both on the control parameter value and on the initial conditions [12,15,16].…”

Section: Stiffness Parameters Are the Control Parametersmentioning

confidence: 99%

Coexisting Regimes in Hysteresis Zone in Platform-Vibrator with Shock

Баженов

Pogorelova

Postnikova

2021

OMTC

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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.

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“…The creation and detailed description of a mathematical model of a platform-vibrator with shock were given in [3][4][5][6]. In previous works, we studied the dynamic behavior of a platform-vibrator with shock when both the system parameters and the parameters of the external exciting force change.…”

Section: Introductionmentioning

confidence: 99%

“…In previous works, we studied the dynamic behavior of a platform-vibrator with shock when both the system parameters and the parameters of the external exciting force change. In [3], we examined the effect of the exciting frequency, in [4], the effect of the technological mass of the mold with concrete, in [5], the effect of the stiffness parameters. In all these cases, interesting nonlinear phenomena that are inherent and often unique to strongly nonlinear non-smooth discontinuous systems were observed.…”

Section: Introductionmentioning

confidence: 99%

Prediction and diagnostics of crises and critical states in an unusual vibro-impact system with soft impact

2022

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In nonlinear dynamical systems, when changing control parameters, critical states may occur. To predict these undesirable events, it is necessary to study the system dynamic behavior with changing in different control parameters. Two-body 2-DOF vibro-impact system is under consideration. The huge mass of the upper body, which can break away from the lower one and be in "free flight" for a short time, may be attributed to its specific and is a cause to consider it unusual. Some changes in the parameters of both external loading and the system itself can increase the efficiency of the machine, the mathematical model of which is the considered vibro-impact system. But the same changes lead to appearance of unwanted nonlinear phenomena, such as permanent sustained chaos, transient chaos, crisis-induced intermittency, and coexisting regimes with larger oscillatory amplitudes. The article shows their occurrence, traces the precursors, carries out their diagnostics by both traditional and less common methods. The description of many numerical experiments is accompanied by numerous figures and tables that clearly and convincingly demonstrate the results obtained. Keywords vibro-impact • crisis • chaotic • intermittency • transient chaos • soft impact • platform vibrator Mathematics Subject Classification (2000) 37G35 • 37N15 • 37L30 • 65T60

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Crisis-Induced Intermittency and Other Nonlinear Dynamics Phenomena in Vibro-impact System with Soft Impact

Cited by 9 publications

References 18 publications

Choice of the Model for Vibro-impact Nonlinear Energy Sink

Choice of the Model for Vibro-impact Nonlinear Energy Sink

Coexisting Regimes in Hysteresis Zone in Platform-Vibrator with Shock

Prediction and diagnostics of crises and critical states in an unusual vibro-impact system with soft impact

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