Lyapunov exponents of impact oscillators with Hertz׳s and Newton׳s contact models

Serweta, Wioleta; Okolewski, Andrzej; Błażejczyk-Okolewska, Barbara; Czołczyński, Krzysztof; Kapitaniak, Tomasz

doi:10.1016/j.ijmecsci.2014.09.007

Cited by 43 publications

(29 citation statements)

References 36 publications

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“…The method presented above let us confirm the usefulness of the basins of attraction calculated for two-dimensional cross-sections of the four-dimensional phase space (presented in Figs. 6,12,13,14). To authenticate that, we compare the probability of reaching given attractor obtained using both methods.…”

Section: Coexistence Of Impacting and Non-impacting Solutionsmentioning

confidence: 99%

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Controlling multistability in coupled systems with soft impacts

Brzeski

Pavlovskaia

Kapitaniak

et al. 2017

International Journal of Mechanical Sciences

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In this paper we present an influence of discontinuous coupling on the dynamics of multistable systems. Our model consists of two periodically forced oscillators that can interact via soft impacts. The controlling parameters are the distance between the oscillators and the difference in the phase of the harmonic excitation. When the distance is large two systems do not collide and a number of different possible solutions can be observed in both of them. When decreasing of the distance, one can observe some transient impacts and then the systems settle down on non-impacting attractor. It is shown that with the properly chosen distance and difference in the phase of the harmonic excitation, the number of possible solutions of the coupled systems can be reduced. The proposed method is robust and applicable in many different systems.

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Section: Coexistence Of Impacting and Non-impacting Solutionsmentioning

confidence: 99%

“…The second approach (soft impact) assumes the finite, nonzero contact time and a penetration of the base by the colliding body. Hence, the contact is modeled as a linear [8,9,10], Hertzian [11,12] or other nonlinear [13] spring and viscous damper. The separate equations of motion describe the in-contact and out-of-contact dynamics.…”

Section: Introductionmentioning

confidence: 99%

Controlling multistability in coupled systems with soft impacts

Brzeski

Pavlovskaia

Kapitaniak

et al. 2017

International Journal of Mechanical Sciences

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show abstract

“…One can distinguish many different approaches coping with the collisions between the rigid bodies. There is a number of continuous models such as Kelvin-Voigt viscoelastic model [22,23], Hertz contact model [24,25] or Mindlin Deresiewicz model [26,27]. These models are based on differential equations which describe the course of collisions.…”

Section: Modeling Of the Clapper To The Bell Impactmentioning

confidence: 99%

Experimental verification of a hybrid dynamical model of the church bell

Brzeski

Kapitaniak

Perlikowski

2015

International Journal of Impact Engineering

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“…An important function used to represent soft impacts is obtained through the Hertz contact theory. Some applications of the Hertz force law in vibro-impact systems are presented in [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Experimental evaluation of a vibro-impact model for two adjacent shear-building structures

et al. 2018

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The vibro-impact phenomenon is found in many engineering applications, from impact of floating ice with ships to rubbing between the stator structure and rotor blades in turbomachinery, and in most cases it is important to know the implication of this phenomenon in the mechanical system. This is often done by proposing vibro-impact models for describing the behavior of the system when subjected to periodically impacts. However, this modelling may be challenging due to the strongly nonlinear characteristics of the impact phenomenon. Therefore, this paper presents a vibro-impact model of two shearbuilding structures positioned side by side, where one of them is driven by an unbalanced DC motor. The structures were modeled using the Euler-Bernoulli beam theory and the contact was modeled based on the Hertz contact theory. In order to validate the model their responses were compared with experimental signals.

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Lyapunov exponents of impact oscillators with Hertz׳s and Newton׳s contact models

Cited by 43 publications

References 36 publications

Controlling multistability in coupled systems with soft impacts

Controlling multistability in coupled systems with soft impacts

Experimental verification of a hybrid dynamical model of the church bell

Experimental evaluation of a vibro-impact model for two adjacent shear-building structures

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