Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

Litak, Grzegorz; Margielewicz, Jerzy; Gąska, Damian; Yurchenko, Daniil; Da̧bek, Krzysztof

doi:10.1007/s11071-020-06023-5

Cited by 12 publications

(5 citation statements)

References 21 publications

(21 reference statements)

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“…A very simplified model for moving a point load by a trolley of an overhead crane is the elliptical pendulum model used in works [7][8][9][10][11][12][13][14][15][16].…”

Section: Literature Review and Problem State-mentmentioning

confidence: 99%

Spatial transportation of the beam on a bifilar fastening

Stadnik¹,

Podlesny²,

Kaporovych³

et al. 2022

FME Transactions

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The complex problem of the spatial motion of the "trolley-beam" mechanical system is investigated. Three stages are considered: 1) movement of the beam on a bifilar suspension to the movable trolley; 2) movement of the beam after the breakage of one branch of the suspension; 3) movement of the beam after the breakage of the second branch of the suspension. The study was carried out by creating mathematical models for each stage of the system movement and then conducting a numerical experiment using computer algebra. The tension of the ropes is calculated at the first and second stages of the system movement. Their extreme values are determined. The obtained results will be used in the further study of the system to reduce the tension of the rope and oscillation amplitude and to prevent accidents.

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“…A very simplified model for moving a point load by a trolley of an overhead crane is the elliptical pendulum model used in works [7][8][9][10][11][12][13][14][15][16].…”

Section: Literature Review and Problem State-mentmentioning

confidence: 99%

Spatial transportation of the beam on a bifilar fastening

Stadnik¹,

Podlesny²,

Kaporovych³

et al. 2022

FME Transactions

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“…It is well known that if an object vibrates harmonically in two directions, plotting these two signals generates what are known as Lissajous figures. Lissajous figures are used to establish the frequency ratio or relative phase between two harmonic signals [16], [17]. Relative phase is the most practical way to measure phase on a machine [8], [9].…”

Section: Introductionmentioning

confidence: 99%

Toward to Vibration Analysis by Knot Theory

Cisneros

2023

icat

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Vibration analysis is one of the most important aspects in the design of structures and mechanical systems, among others, subject to dynamic loads. As well as for the analysis of failures caused by vibratory aspects. A good performance of an industrial system is often associated with the availability of mathematical models of the dynamic behaviour of the system. In some situations, the complexity of the processes makes it difficult to have models that help us to analyse these processes. This paper proposes the use of knot theory, which is a topological tool, for vibration analysis. This topological tool, in this case, associates a topological invariant when there is a drastic change in vibrations. The present work is based on the fact that it is well known that the equations representing harmonic motion generate Lissajous figures. In knot theory, there are several classifications of knots, one of these classifications is known as Lissajous knots. The use of this tool is shown in the supposition that we have a system represented by three equations of the form f(t) = Acos(Bt + C) , where with the indicated parameters it generates a knot (being its nominal value). Making a change in the phase, which represents a fault, generates a different knot than the nominal knot. One of the advantages of this proposed method is that it is not necessary to have the model, and one of the disadvantages by nature of this method is that three signals are required to use this topological tool.

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“…Pendulum systems are very popular non-linear systems used in scientific and other applications. For example, the payload dynamics in overhead cranes or jib cranes can be understood as examples of pendulums [ 1 , 2 ]. With suitable excitation and damping, such systems are strongly non-linear, exhibiting a variety of solutions, including oscillations and rotations.…”

Section: Introductionmentioning

confidence: 99%

Dynamics and Entropy Analysis of a Frictionally Loaded Pendulum

Litak

Borowiec

Da̧bek

2022

Entropy

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We use friction to simultaneously damp and excite a pendulum system. A Froude pendulum attached to a suspension shaft is subjected to a frictional load. We investigate two types of response of the system: regular and chaotic responses, depending on the excitation frequency. A transient chaotic solution was also obtained. We identify the motions using phase portraits, Poincaré maps, and Fourier spectra. Finally, the composite multiscaled entropy was estimated for the specified cases to confirm the preliminary classification.

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Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

Cited by 12 publications

References 21 publications

Spatial transportation of the beam on a bifilar fastening

Spatial transportation of the beam on a bifilar fastening

Toward to Vibration Analysis by Knot Theory

Dynamics and Entropy Analysis of a Frictionally Loaded Pendulum

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