On a cascade of autoresonances in an elevator cable system

Sandilo, Sajad H.; Horssen, Wim T. van

doi:10.1007/s11071-015-1966-8

Cited by 37 publications

(28 citation statements)

References 36 publications

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“…After first studies for the purpose of particles accelerations [1][2][3], autoresonance has become a very active field of research in different areas of natural science and engineering, from celestial mechanics [4][5][6] and plasmas [6][7][8] to mechanical structures [9,10]. Over the years, the attention was focused on physical processes described as oscillator chains with the low number of particles.…”

Section: Introductionmentioning

confidence: 99%

Resonance-Induced Energy Localization in Weakly Dissipative Anharmonic Chains

Kovaleva

2020

Nonlinear Dynamics of Structures, Systems and Devices

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HIGHLIGHTS A weakly dissipative nonlinear chain driven by harmonic forcing with a slowlyvarying frequency chain demonstrates autoresonance in a bounded time interval. The emergence and the duration of autoresonance depend on the interplay between the structural and excitation parameters. Autoresonant energy localization with energy equipartition between the autoresonant oscillators in the entire chain or in a part of the chain is observed. AbstractIn this work, we develop an analytical framework to explain the influence of dissipation and detuning parameters on the emergence and stability of autoresonance in a strongly nonlinear weakly damped chain subjected to harmonic forcing with a slowly-varying frequency. Using the asymptotic procedures, we construct the evolutionary equations, which describe the behavior of the array under the condition of 1:1 resonance and then approximately compute the slow amplitudes and phases as well as the duration of autoresonance. It is shown that, in contrast to autoresonance in a nondissipative chain with unbounded growth of energy, the energy in a weakly damped array being initially at rest is growing only in a bounded time interval up to an instant of simultaneous escape from resonance of all autoresonant oscillators. Analytical conditions of the emergence and stability of autoresonance are confirmed by numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Resonance-Induced Energy Localization in Weakly Dissipative Anharmonic Chains

Kovaleva

2020

Nonlinear Dynamics of Structures, Systems and Devices

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“…Miranker [1] was the first who developed the mathematical equations of motion for laterals oscillations of axially accelerating string. For further studies on vibrations of string and beams, the reader is referred the papers [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. To suppress the vibrations and noise in structures and machines, damping of string material is widely taken into consideration [17].…”

Section: Introductionmentioning

confidence: 99%

“…[10] examined the viscous damping via two timescales perturbation method. Gaiko and van Horssen [5] used the method of Laplace transform and two timescale perturbation method to investigate the transversal vibrations of traveling string with the boundary damping. Fung et.…”

Section: Introductionmentioning

confidence: 99%

On (Non) Applicability of a Mode-Truncation of a Damped Traveling String

Malookani

Sandilo

Hanan³

2019

Mehran Univ. res. j. eng. technol.

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This study investigates a linear homogeneous initial-boundary value problem for a traveling stringunder linear viscous damping. The string is assumed to be traveling with constant speed, while it is fixed at both ends. Physically, this problem represents the vertical (lateral) vibrations of damped axially moving materials. The axial belt speed is taken to be positive, constant and small in comparison with a wave speed, and the damping is also considered relatively small. A two timescale perturbation method together with the characteristic coordinate's method will be employed to establish the approximateanalytic solutions. The damped amplitude-response of the system will be computed under specific initial conditions. The obtained results are compared with the finite difference numerical technique for justification. It turned out that the introduced damping has a significant effect on the amplitude-response.Additionally, it is proven that the mode-truncation is applicable for the damped axially traveling string system on a timescale of order  -1 .

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“…Benosman and Fukui (2014) have studied numerically the problem of elevator rope with sway motion due to external force disturbances through an active control, by using nonlinear controllers based on Lyapunov theory, to stabilise the rope sway dynamics. A model for transversal vibrations of an elevator cable system is studied in Sandilo and van Horssen (2015). Chang et al (2011) investigated a high-speed elevator system in order to examine the characteristics of the excitations and analyse the dynamic responses due to horizontal vibration generated from the elevator wheels running on rough and winding guide rails.…”

Section: Introductionmentioning

confidence: 99%

Active vibration control of an elevator system using magnetorheological damper actuator

Tusset¹,

Santo²,

Balthazar³

et al. 2017

IJNDC

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Abstract:We investigated the horizontal response of a vertical transportation with nonlinearities under excitation by guide rail deformations. A LQR control strategy was used in order to improve the comfort of passengers. To this end, a magnetorheological damper (MR damper) was used. The control force of the damper is a function of the voltage applied in the coil of the MR damper that is based on the force given by the controller. Numerical simulations were performed to investigate the nonlinear behaviour of the adopted mathematical model. Moreover, other issues such as robustness of the control technique were evaluated considering parametric errors and noise measurement. The results show that the LQR control strategy using MR damper can be effective in reducing the vibration of the vertical transport.Keywords: optimal feedback control; vertical transportation; MR damper; high-speed elevator; parametric uncertainties; wavelet-based scale index; nonlinear model; chaos; LQR control; nonlinear dynamics.

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On a cascade of autoresonances in an elevator cable system

Cited by 37 publications

References 36 publications

Resonance-Induced Energy Localization in Weakly Dissipative Anharmonic Chains

Resonance-Induced Energy Localization in Weakly Dissipative Anharmonic Chains

On (Non) Applicability of a Mode-Truncation of a Damped Traveling String

Active vibration control of an elevator system using magnetorheological damper actuator

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