Nonlinear Dynamics of Electro-mechanical System Composed of Two Pendulums and Rotating Hub

Szmit, Zofia; Warmiński, Jerzy

doi:10.1016/j.proeng.2016.05.122

Cited by 16 publications

(4 citation statements)

References 6 publications

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“…The time step has been fixed as constant for each frequency and equal to 1/40 of the excitation period. Examples of numerical frequency-response curves for the considered case, similar to those obtained in [17], are reported in forthcoming Fig. 9, where they are compared with their analytical counterparts.…”

Section: Numerical Approach: Finite Element Methodsmentioning

confidence: 90%

Nonlinear dynamics of a planar beam–spring system: analytical and numerical approaches

2018

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The multiple timescales method is applied to the exact partial differential equations of the planar motion of a hinged-simply supported beam with a linear axial spring of arbitrary stiffness. The forceddamped and free oscillations of the system around frequencies corresponding to nth natural bending mode are examined thoroughly and compared with numerical simulations as well as with already published results obtained by Lindstedt-Poincaré method. A special numerical technique using explicit finite element method to draw the frequency-response curves is appositely developed. The well-known jump phenomena between resonant and non-resonant branches, as well as superharmonic resonances, have been detected numerically.

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Section: Numerical Approach: Finite Element Methodsmentioning

confidence: 90%

Nonlinear dynamics of a planar beam–spring system: analytical and numerical approaches

2018

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“…Bifurcations in mechanical systems have been the subject of numerous studies in the field of nonlinear dynamics. Researchers have paid particular attention to systems such as pendulums [1][2][3], aeroelastic systems [4][5][6], plates [7,8] and beams [9]. However, important bifurcation phenomena also occur in other types of mechanical systems, such as brakes [10] or gears [11].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Bifurcation Vibrations of an Industrial Robot Arm System with Joints Compliance

Gierlak,

Warmiński

2023

Applied Sciences

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This paper deals with the analysis of nonlinear vibration phenomena in the arm system of an industrial robot. The presented mathematical model of the robot takes into account the flexibility of the joints, which results in low-frequency vibrations in the arm. The study of vibration phenomena has been carried out using analytical, numerical and experimental methods. Special attention has been paid to bifurcation phenomena. The influence of two bifurcation parameters on the behaviour of the robot arm was studied. It was shown that the amplitude and frequency of the harmonic excitation create a nonlinear effect on the vibration amplitudes of the links. In bifurcation regions, the vibration amplitudes can even differ several times depending on the direction of changes in the bifurcation parameter. In general, the results indicate that, contrary to common practice, it is worth paying attention to nonlinear phenomena when analysing robot vibrations.

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“…The interest in the dynamic behavior of electromechanical nonlinear systems is not a new, being explored in open literature [3,7,13,34,38,40,57,69,71,73,79] and classical books [1,41,47,52] for decades. Despite that, many modern applications of engineering and science are based on the interaction between an electric system with a mechanical counterpart, such as energy harvesting technologies [15,16,17,25,28,45,55,61,62], micro/nano electromechanical resonators [39,64,82,83,84], drill-strings [21,53] etc.…”

Section: Introductionmentioning

confidence: 99%

On the reduction of nonlinear electromechanical systems

Cunha,

Pereira,

Avanço

et al. 2022

Preprint

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The present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach and clarifying some confusing points found in the literature. Expressions for the characteristic time scales of dynamics are deduced from a physical analysis that establishes an analogy between electromechanical dynamics and the kinetics of a chemical reaction. It provides a physical justification, supplemented by non-dimensionalization and scaling of the equations, to reduce the dynamics of interest by assuming a quasi-steady state for the electrical subsystem, eliminating the inductive term from the electrical equation. Numerical experiments help to illustrate the typical behavior of the electromechanical

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Nonlinear Dynamics of Electro-mechanical System Composed of Two Pendulums and Rotating Hub

Cited by 16 publications

References 6 publications

Nonlinear dynamics of a planar beam–spring system: analytical and numerical approaches

Nonlinear dynamics of a planar beam–spring system: analytical and numerical approaches

Analysis of Bifurcation Vibrations of an Industrial Robot Arm System with Joints Compliance

On the reduction of nonlinear electromechanical systems

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