Dynamics and control of periodic and non-periodic behavior of Duffing vibrating system with fractional damping and excited by a non-ideal motor

Varanis, Marcus; Tusset, Ângelo Marcelo; Balthazar, José Manoel; Litak, Grzegorz; Oliveira, Clivaldo; Rocha, Rodrigo Tumolin; Nabarrete, Airton; Piccirillo, Vinícius

doi:10.1016/j.jfranklin.2019.11.048

Cited by 20 publications

(11 citation statements)

References 42 publications

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“…Such an approach becomes problematic for multi-variable nonlinear systems having a wide spectrum of possible steady-state responses that change (bifurcate) with slowly varying parameters. Verification of periodic (or oscillatory chaotic) responses in such cases is done by numerical methods, often with a parallel computing approach [ 3 , 4 ]. Determining bifurcations of nonlinear dynamical systems often require a sophisticated computational approach to visualize the obtained results [ 5 , 6 ].…”

Section: Introductionmentioning

confidence: 99%

“…Typical visualization of those changes when one parameter varies slowly has the form of one-parameter bifurcation diagrams (figures) with the varying parameter representing the horizontal axis while the vertical axis is a certain quantity characterizing the changing responses. That quantity could be the identified maximum values of the response in a chosen time interval, the output of the 0–1 test for chaos (a number between 0 (for periodic responses) and 1 (for chaotic ones)), the frequency of periodic output, entropy or others [ 4 ]. In this paper, we illustrate our bifurcation diagrams (mostly with two slowly varying parameters) with the use of an interesting autonomous system described in Appendix A .…”

Section: Introductionmentioning

confidence: 99%

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Computational Analysis of Ca2+ Oscillatory Bio-Signals: Two-Parameter Bifurcation Diagrams

Marszałek

Sadecki

Walczak

2021

Entropy

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Two types of bifurcation diagrams of cytosolic calcium nonlinear oscillatory systems are presented in rectangular areas determined by two slowly varying parameters. Verification of the periodic dynamics in the two-parameter areas requires solving the underlying model a few hundred thousand or a few million times, depending on the assumed resolution of the desired diagrams (color bifurcation figures). One type of diagram shows period-n oscillations, that is, periodic oscillations having n maximum values in one period. The second type of diagram shows frequency distributions in the rectangular areas. Each of those types of diagrams gives different information regarding the analyzed autonomous systems and they complement each other. In some parts of the considered rectangular areas, the analyzed systems may exhibit non-periodic steady-state solutions, i.e., constant (equilibrium points), oscillatory chaotic or unstable solutions. The identification process distinguishes the later types from the former one (periodic). Our bifurcation diagrams complement other possible two-parameter diagrams one may create for the same autonomous systems, for example, the diagrams of Lyapunov exponents, Ls diagrams for mixed-mode oscillations or the 0–1 test for chaos and sample entropy diagrams. Computing our two-parameter bifurcation diagrams in practice and determining the areas of periodicity is based on using an appropriate numerical solver of the underlying mathematical model (system of differential equations) with an adaptive (or constant) step-size of integration, using parallel computations. The case presented in this paper is illustrated by the diagrams for an autonomous dynamical model for cytosolic calcium oscillations, an interesting nonlinear model with three dynamical variables, sixteen parameters and various nonlinear terms of polynomial and rational types. The identified frequency of oscillations may increase or decrease a few hundred times within the assumed range of parameters, which is a rather unusual property. Such a dynamical model of cytosolic calcium oscillations, with mitochondria included, is an important model in which control of the basic functions of cells is achieved through the Ca2+ signal regulation.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computational Analysis of Ca2+ Oscillatory Bio-Signals: Two-Parameter Bifurcation Diagrams

Marszałek

Sadecki

Walczak

2021

Entropy

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“…In this paper, the responses of a portal frame excited by an unbalanced DC motor are measured and analyzed in the time and frequency domain [5]. Time-frequency analysis methods have been successfully used to characterize nonlinearities in the mechanical system [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

A Short Note on Synchrosqueezed Transforms for Resonant Capture, Sommerfeld Effect and Nonlinear Jump Characterization in Mechanical Systems

Varanis¹,

Silva²,

Balthazar³

et al. 2021

J. Vib. Eng. Technol.

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Background Several applications in engineering, a mechanical system operates in the nonstationary regime, creating the possibility to generate nonlinearities in them. Time frequency analysis methods are using the processing of signals of a nonstationary nature, as well as for the characterization of nonlinearities in mechanical systems. A particular phenomenon seen in nonstationary systems is the Sommerfeld effect, which occurs due to the nonlinear interaction between a non-ideal energy source and a mechanical system. Purpose In this research we explore the use of synchronized wavelet transform for the characterization of the Sommerfeld effect and nonlinear jump phenomenon in mechanical systems in the frequency domain. Methods Nonstationary signals were measured on a 3-DOF shear build structure. We applied the wavelet synchrosqueezed transform for Resonant Capture, Sommerfeld Effect and Nonlinear Jump Characterization. Results It is shown how the results of the synchrotron wavelet transform is more efficient than those of classical methods. Furthermore, the mother wavelet has little influence on the SWT-based results. ConclusionThe synchrosqueezed transform has the potential to characterization nonlinear parameters in nonstationary signals, in particular, resonant capture, Sommerfeld effect, and nonlinear jump. Further research should focus on overcoming issues in the SWT technique to improve parameter estimation of mechanical systems.

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“…Moreover, the microelectromechanical systems (MEMS) topics are investigated [31]. The wavelet transform has been used for the analysis of the Sommerfeld effect with only time response and control design proposed by Varanis et al [32,33].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Coupled Torsion/Lateral Vibration and Sommerfeld Behavior in a Double U-Joint Driveshaft

Yao

DeSmidt

2020

Journal of Vibration and Acoustics

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Many driveline systems are designed to accommodate angular misalignment by use of flexible couplings or Universal Joints (U-Joints) which link individual shaft segments. The Sommerfeld effect is a nonlinear phenomena observed in some rotor systems being driven through a critical speed when there is not enough power to accelerate the rotor through resonance. Previous studies have shown that rotor speed can become captured when transitioning through natural frequencies due to nonlinear interactions between a non-ideal driving input and rotor imbalance. This paper, for the first time, shows that this type of rotor speed capture phenomena can also be induced by driveline misalignment. During rotor spinup under constant motor torque it is found that misalignment-induced rotor speed capture phenomena can occur as the shaft speed approaches ½ the first elastic torsional natural frequency. Depending on misalignment level and motor torque, the shaft speed will either dwell near this speed and then pass through, or the speed will become trapped. Here a nonlinear rotordynamics model of a segmented driveshaft connected by two U-Joints including effects of angular misalignment and load torque is developed for the study. This analysis also determines the minimum driveline misalignment angle for which the shaft speed capture phenomena will occur for a given motor torque and load torque condition.

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Dynamics and control of periodic and non-periodic behavior of Duffing vibrating system with fractional damping and excited by a non-ideal motor

Cited by 20 publications

References 42 publications

Computational Analysis of Ca2+ Oscillatory Bio-Signals: Two-Parameter Bifurcation Diagrams

Computational Analysis of Ca2+ Oscillatory Bio-Signals: Two-Parameter Bifurcation Diagrams

A Short Note on Synchrosqueezed Transforms for Resonant Capture, Sommerfeld Effect and Nonlinear Jump Characterization in Mechanical Systems

Nonlinear Coupled Torsion/Lateral Vibration and Sommerfeld Behavior in a Double U-Joint Driveshaft

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