Experiments and numerical results on non-linear vibrations of an impacting Hertzian contact. Part 1: harmonic excitation

Rigaud, Emmanuel; Perret-Liaudet, Joël

doi:10.1016/s0022-460x(02)01262-2

Cited by 83 publications

(44 citation statements)

References 11 publications

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“…The experimental natural frequency is close to the theoretical one since the relative error is less than 0.15 %, and the damping ratio value is coherent with preceding studies [1][2]6]. …”

Section: Measured Natural Frequency and Damping Ratiosupporting

confidence: 90%

Response of an impacting Hertzian contact to an order-2 subharmonic excitation : Theory and experiments

Perret-Liaudet

Rigaud

2006

Journal of Sound and Vibration

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In this paper, the response of a normally excited preloaded Hertzian contact is investigated in order to analyze the subharmonic resonance of order 2. The nonlinearity associated with contact losses is included. The method of multiple scales is used to obtain the non-trivial steady state solutions, their stability, and the frequency-response curves. To this end, a third order Taylor series of the elastic Hertzian contact force is introduced over the displacement interval where the system remains in contact. A classical time integration method is also used in conjunction with a shooting method to take into account losses of contact. The theoretical results show that the subharmonic resonance constitutes a precursor of dynamic responses characterised by loss of contact, and consequently, the resonance establishes over a wide frequency range. Finally, experimental validations are also presented in this paper. To this end, a specific test rig is used. It corresponds to a double sphere-plane contact preloaded by the weight of a moving mass. Experimental results show good agreements with theoretical ones.

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“…The experimental natural frequency is close to the theoretical one since the relative error is less than 0.15 %, and the damping ratio value is coherent with preceding studies [1][2]6]. …”

Section: Measured Natural Frequency and Damping Ratiosupporting

confidence: 90%

Response of an impacting Hertzian contact to an order-2 subharmonic excitation : Theory and experiments

Perret-Liaudet

Rigaud

2006

Journal of Sound and Vibration

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“…Parallel connection of hysterons W j with weights ξ j we call the converter W with an area of permissible states (5) such that for every initial state (6) all the continuous scalar inputs u(t) (t t 0 ) that satisfy the condition u(t 0 ) = u 0 are allowed. The output is determined by the relation…”

Section: Hysteretic Materialsmentioning

confidence: 99%

“…However, this type of damping has a significant drawback, namely the low efficiency outside the region of resonance of the system. One way to solve this problem is to use a nonlinear viscous damper [1][2][3][4][5] or damper with hysteretic properties. It should also be pointed out the exciting and interesting (generally, from the fundamental point of view) model of a e-mail: mkl150@mail.ru b e-mail: melechp@yandex.ru viscous damping which is based on the technique of fractional derivatives and can be called as a fractional damping [6,7].…”

Section: Introductionmentioning

confidence: 99%

Hysteretic damper based on the Ishlinsky-Prandtl model

et al. 2016

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“…This approach allows to develop and to analyze the common form of motion equations for vibroimpact systems elements and to describe the full set of realized movements on all timebase, including the impact time. In such works as [6,7,25] the authors describe the use and limitations of this theory. The Hertz theory is used for impact rule writing in [26][27][28], for example, for singledegree-of-freedom vibroimpact systems more often.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Two Impact Simulation Methods Used for Nonlinear Vibroimpact Systems with Rigid and Soft Impacts

Баженов

Pogorelova

Postnikova

2013

Journal of Nonlinear Dynamics

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This paper compares the use of two impact simulation methods for two-degree-of-freedom nonlinear vibroimpact systems with rigid and soft impacts. These methods are (I) impact simulation by boundary conditions with the use of Newton's restitution coefficient based on stereomechanic shock theory and (II) impact simulation by contact interaction force based on quasistatic Hertz's contact theory. It is shown that both methods are applied and give the coinciding results for system with elastic rigid impact under periodic external loading. Loading curves built by parameter continuation method are confirming this result. Impact simulation by the second method is also fulfilled for vibroimpact system with rigid impact under random external loading. For vibroimpact system with soft impact, the simulation of impact by the second method gives a better result. The application of linear elastic force as contact one is possible too but the use of Hertz's contact force is more preferable. The authors consider that the impact simulation by Hertz contact interaction force gives good results for nonlinear vibroimpact systems with impacts of any kind if all limitations with Hertz's law used are observed.

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Experiments and numerical results on non-linear vibrations of an impacting Hertzian contact. Part 1: harmonic excitation

Abstract: SummaryThe purpose of this paper is to investigate experimental and numerical dynamic responses

Cited by 83 publications

References 11 publications

Response of an impacting Hertzian contact to an order-2 subharmonic excitation : Theory and experiments

Response of an impacting Hertzian contact to an order-2 subharmonic excitation : Theory and experiments

Hysteretic damper based on the Ishlinsky-Prandtl model

Comparison of Two Impact Simulation Methods Used for Nonlinear Vibroimpact Systems with Rigid and Soft Impacts

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