Escape in a nonideal electro-mechanical system

Belato, D.; Weber, Hans Ingo; Balthazar, José Manoel

doi:10.1590/s0100-73862002000400014

Cited by 3 publications

(9 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The difference between the present paper and Belato et al [12,13] is that the latter made the analysis only for specific resonant frequencies, while the present paper varies the excitation frequency and obtain bifurcations diagrams. The present paper also provides basins of attraction, which is not present in Belato et al [12,13].…”

Section: Introductionmentioning

confidence: 77%

“…The differential equations obtained with the coordinate a and h are represented by Eqs. (12) and 13:…”

Section: Dynamical Modelmentioning

confidence: 99%

“…In Kransnopolskaya and Shvets [5] and Belato et al [12,13], it was analyzed the mechanism represented in Fig. 1, where a crank-slider mechanism powered by a DC motor moves horizontally the point of suspension of a pendulum.…”

Section: Introductionmentioning

confidence: 99%

“…In Belato et al [12], due to the power limitation of the motor, the frequency of the pendulum was being captured at resonance, modifying the final response of the system. It was found a saddle-node bifurcation on the resonant region before the chaos rises.…”

Section: Introductionmentioning

confidence: 99%

“…In a recent paper, Tusset et al [18] analyzed a pendular mechanism with a nonideal source of energy and proposed a control with State-Dependent Riccati Equation (SDRE). This mechanism consisted of a block moving horizontally linked to an eccentric mass rotating on the center powered by a DC motor and the third mass is a pendulum suspended below the block.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors

Avanço

Tusset

Balthazar

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

This study analyzes a nonlinear system with a crankshaft -slider mechanism linked to a pendulum. The crank is powered by a DC motor that moves horizontally the pendulum pivot. The speed of the motor is influenced by the pendulum dynamics, reason for calling the system as nonideal. In literature, the vibration of the pendulum support by a crank-shaftslider is generally considered as harmonic what neglects the real complexity of the mechanism. It is also common, for the crank speed or the excitation frequency to be considered constant, so a unique degree-of-freedom can take place. The novelty in this research is the analysis of the feedback effect of the pendulum over the crank speed and the complexity of crank-slider mechanism without approaching to a harmonic motion. Different types of motion occur as oscillations, rotations, and chaos. Results with different initial conditions are worked out and basins of attractions plotted. Chaos was obtained when small variations of parameters are made. The methods of analysis include phase portraits, time histories, bifurcations diagrams, and basins of attraction. The verification of chaotic phenomena is performed through the 0-1 test. By the end, the feedback control is applied using the method of Tereshko by altering the energy of the chaotic system, leading the pendulum to a limit cycle.

show abstract

Section: Introductionmentioning

confidence: 77%

“…The differential equations obtained with the coordinate a and h are represented by Eqs. (12) and 13:…”

Section: Dynamical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors

Avanço

Tusset

Balthazar

et al. 2018

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

show abstract

Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone

Avanço

Balthazar

Tusset³

et al. 2021

Z Angew Math Mech

View full text Add to dashboard Cite

The parametric pendulum and others different pendular mechanisms were extensively analyzed in current literature because of the chaotic motions.Recently, practical reasons, like energy harvesting, motivated the study of some pendular systems. The resonance and the chaos may occur in multiple and submultiple frequencies based on the natural frequency of the pendulum. In the present paper, a double pendulum is analyzed with two subharmonic frequencies and in the main resonance zone. The results found demonstrate high similarities of the double pendulum with the parametric pendulum when compared the bifurcation diagrams based on varying the amplitude. The conditions in the numerical simulation include a variation in the viscous friction in the joints and different amplitudes and frequency of excitation. The differential equations used dimensionless parameters representing time, frequency, amplitude, friction, position and velocities. Concerning the results, all tests performed have pointed that the same type of motion takes place in the two pendulums after the transient time have already elapsed.

show abstract

Dynamics of a non-ideally driven oscillating system under frictional slip

Chakraborty,

Bhattacharyya

2023

Journal of Vibration and Control

View full text Add to dashboard Cite

The Sommerfeld Effect pertains to the non-linear jump phenomenon near the resonance frequency of an excited structure powered by a non-ideal drive that is incapable to supply the required power to the oscillating sub-system. Often this situation is dealt with by increasing the viscous damping present in the system at the expense of considerable power loss. However, the use of non-viscous damping for the attenuation of the Sommerfeld Effect is considered in very few articles. In this paper, the dynamics of a non-ideal DC motor-driven vibrating system with frictional slip as the dissipation element is presented. Use of the method of multiple time scales is employed to find the response of the system semi-analytically. The non-linear dynamical characteristics of the response as the motor speed crosses the resonance condition is analyzed using the linear stability analysis and subsequently, the obtained response is verified using numerical results. The transition of the operating condition between stable and unstable zones and the post-resonance dynamic behavior of such systems indicated that under proper parametric condition, it is possible to achieve a smooth variation of operating speed via a combination of stick and slip motion. Furthermore, the rate of voltage increment is also found to play a pivotal role in surpassing the critical speed of the system.

show abstract

Escape in a nonideal electro-mechanical system

Cited by 3 publications

References 9 publications

On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors

On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors

Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone

Dynamics of a non-ideally driven oscillating system under frictional slip

Contact Info

Product

Resources

About