Control of a Forced Impacting Hertzian Contact Oscillator Near Sub- and Superharmonic Resonances of Order 2

Bichri, Amine; Belhaq, Mohamed

doi:10.1115/1.4004309

Cited by 12 publications

(6 citation statements)

References 22 publications

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“…It was shown that the excitation from above or through base displacement shifts the resonance curve left, whereas the fast parametric stiffness shifts the response curve right. A recent study was carried out near sub-and superharmonic resonances of order 2 and similar phenomena were found [10]. The results demonstrated principally that such control techniques produce a shift and softens the system behavior.…”

Section: Introductionsupporting

confidence: 61%

Effect of time delay on vibroimpact dynamics in a forced Hertzian contact oscillator

Mokni

Bichri

Belhaq

2012

MATEC Web of Conferences

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Abstract. Vibroimpact dynamics of a forced single-sided Hertzian contact oscillator are typically initiated by jumps phenomena near resonances. It was shown that high-frequency excitations can be used to shift the threshold of such vibroimpacts toward higher or lower frequencies of the basic excitation depending on the type of the high-frequency excitation. These excitations not only produce a shift, but also soften the system behavior. The present paper investigates the effect of time delay state feedback on the threshold of vibroimpact dynamics of a forced Hertzian contact oscillator near the primary resonance. It is shown that for certain combinations of the gain parameters of delay state feedback, the jumps disappear leading the system to be maintained in contact when the excitation frequency sweeps through the resonance.

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Section: Introductionsupporting

confidence: 61%

Effect of time delay on vibroimpact dynamics in a forced Hertzian contact oscillator

Mokni

Bichri

Belhaq

2012

MATEC Web of Conferences

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“…The practical way for controlling the vibroimpact dynamics of a Hertzian contact forced oscillator is the introduction of a fast harmonic base displacement, as showed by Bichri et al [11], which is generally around some microns. Different aspects of vibroimpact dynamics in a forced Hertzian contact oscillator such as the effect of time delay, control of a forced impact Hertzian contact near resonances [12], contact stiffness modulation in contact-mode atomic force microscopy [13], and the effect of EA on contact loss in a Hertzian contact oscillator [14] are intensively investigated.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation

et al. 2023

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In this work, the effect of vibro-impact nonlinear, forced, and damped oscillator on the dynamics of the electromagnetic actuation (EA) near primary resonance is studied. The vibro-impact regime is given by the presence of the Hertzian contact. The EA is supplied by a constant current generating a static force and by an actuation generating a fast alternative force. The deformations between the solids in contact are supposed to be elastic and the contact is maintained. In this study, a single degree of freedom nonlinear damped oscillator under a static normal load is considered. An analytical approximate solution of this problem is obtained using the Optimal Auxiliary Functions Method (OAFM). By means of some auxiliary functions and introducing so-called convergence-control parameters, a very accurate approximate solution of the governing equation can be obtained. We need only the first iteration for this technique, applying a rigorous mathematical procedure in finding the optimal values of the convergence-control parameters. Local stability by means of the Routh-Hurwitz criteria and global stability using the Lyapunov function are also studied. It should be emphasized that the amplitude of AC excitation voltage is not considered much lower than bias voltage (in contrast to other studies). Also, the Hertzian contact coupled with EA is analytically studied for the first time in the present work. The approximate analytical solution is determined with a high accuracy on two domains. Local stability is established in five cases with some cases depending on the trace of the Jacobian matrix and of the discriminant of the characteristic equation. In the study of global stability, the estimate parameters which are components of the Lyapunov function are given in a closed form and a graphical form and therefore the Lyapunov function is well-determined.

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“…The super-and sub-harmonic resonance conditions along with the combination resonances, have been studied by Elnaggar and El-Basyouny [22] for the additive type of self-excited two coupled-second order systems subjected to multi-frequency excitation. These resonance conditions for the effect of fast harmonic base displacement with periodically time varying stiffness on Vibro impact dynamics of a forced single-sided Hertzian contact oscillator have been investigated by Bichri and Belhaq [23]. Davis and Rajan [24,25] discussed the random sub and superharmonic resonance conditions extensively with the help of a Duffing oscillator.…”

Section: Introductionmentioning

confidence: 99%

Pneumatic Artificial Muscle Actuator Under Parametric and Hard Excitations

Kalita¹,

Dwivedy²

2021

Preprint

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In this work, a single degree of freedom system consisting of a mass and a Pneumatic Artificial Muscle (PAM) subjected to time varying pressure inside the muscle is considered. The system is subjected to hard excitation and the governing equation of motion is found to be that of a nonlinear forced and parametrically excited system under super- and sub-harmonic resonance conditions. The solution of the nonlinear governing equation of motion is obtained using the method of multiple scales (MMS). The time and frequency response, phase portraits and basin of attraction have been plotted to study the system response along with the stability and bifurcations. Further, the different muscle parameters have been evaluated by performing experiments which are further used for numerically evaluating the system response using the theoretically obtained closed form equations. The responses obtained from the experiments are found to be in good agreement with those obtained from the method of multiple scales. With the help of examples, the procedure to obtain the safe operating range of different system parameters have been illustrated.

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Control of a Forced Impacting Hertzian Contact Oscillator Near Sub- and Superharmonic Resonances of Order 2

Cited by 12 publications

References 22 publications

Effect of time delay on vibroimpact dynamics in a forced Hertzian contact oscillator

Effect of time delay on vibroimpact dynamics in a forced Hertzian contact oscillator

Analysis of the Vibro-Impact Nonlinear Damped and Forced Oscillator in the Dynamics of the Electromagnetic Actuation

Pneumatic Artificial Muscle Actuator Under Parametric and Hard Excitations

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