Bifurcation study of a chaotic model variable-length pendulum on a vibrating base

Krasilnikov, P. S.; Gurina, Tatyana; Svetlova, Viktoriya

doi:10.1016/j.ijnonlinmec.2018.06.011

Cited by 13 publications

(10 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now, we will look at the variablelength pendulum with stiffness and damping as investigated by different authors. In [36] one finds an analysis without the damping force, while [37][38][39], and [40] include damping force in the analysis.…”

Section: If Resonance Appears At Frequencymentioning

confidence: 99%

“…In [36] the equation y = a sin t for modeling a pendulum harmonic oscillations (as shown in Fig. 11) is considered.…”

Section: Variable-length Pendulum With Stiffness and Dampingmentioning

confidence: 99%

“…The differential equations of dynamics are derived from the sum of kinetic energy and the rigid pendulum's potential energy for both the first and second mutation. Also (36) where l-the pendulum elongation, l 0 -constant length, x-the slider displacement, φ is the angular velocity, φ is the angular acceleration, and M is the mass of the slider body.…”

Section: Variable-length Pendulum With Stiffness and Dampingmentioning

confidence: 99%

See 2 more Smart Citations

On the Modeling and Simulation of Variable-Length Pendulum Systems: A Review

Yakubu

Olejnik

Awrejcewicz

2022

Arch Computat Methods Eng

View full text Add to dashboard Cite

A comprehensive review of variable-length pendulums is presented. An attempt at a unique evaluation of current trends in this field is carried out in accordance with mathematical modeling, dynamical analysis, and original computer simulations. Perspectives of future trends are also noted on the basis of various concepts and possible theoretical and engineering applications. Some important physical concepts are verified using dedicated numerical procedures and assessed based on dynamical analysis. At the end of the review, it is concluded that many variable-length pendulums are very demanding in the modeling and analysis of parametric dynamical systems, but basic knowledge about constant-length pendulums can be used as a good starting point in providing much accurate mathematical description of physical processes. Finally, an extended model for a variable-length pendulum’s mechanical application being derived from the Swinging Atwood Machine is proposed. The extended SAM presents a novel SAM concept being derived from a variable-length double pendulum with a suspension between the two pendulums. The results of original numerical simulations show that the extended SAM’s nonlinear dynamics presented in the current work can be thoroughly studied, and more modifications can be achieved. The new technique can reduce residual vibrations through damping when the desired level of the crane is reached. It can also be applied in simple mechatronic and robotic systems.

show abstract

Section: If Resonance Appears At Frequencymentioning

confidence: 99%

“…In [36] the equation y = a sin t for modeling a pendulum harmonic oscillations (as shown in Fig. 11) is considered.…”

Section: Variable-length Pendulum With Stiffness and Dampingmentioning

confidence: 99%

Section: Variable-length Pendulum With Stiffness and Dampingmentioning

confidence: 99%

See 1 more Smart Citation

On the Modeling and Simulation of Variable-Length Pendulum Systems: A Review

Yakubu

Olejnik

Awrejcewicz

2022

Arch Computat Methods Eng

View full text Add to dashboard Cite

show abstract

“…Krasilnkov presents in [15] the variable-length pendulum harmonic oscillations, which depend on the length of the pendulum. Lyapunov exponents, bifurcation diagrams, and the Poincaré maps situated on phase plane diagrams were used to inspect the system behavior.…”

Section: Introductionmentioning

confidence: 99%

Modeling, Simulation, and Analysis of a Variable-Length Pendulum Water Pump

2021

View full text Add to dashboard Cite

Due to the long-term problem of electricity and potable water in most developing and undeveloped countries, predominantly rural areas, a novelty of the pendulum water pump, which uses a vertically excited parametric pendulum with variable-length using a sinusoidal excitation as a vibrating machine, is presented. With this, more oscillations can be achieved, reducing human effort further and having high output than the existing pendulum water pump with the conventional pendulum. The pendulum, lever, and piston assembly are modeled by a separate dynamical system and then joined into the many degrees-of-freedom dynamical systems. The present work includes friction while studying the system dynamics and then simulated to verify the system’s harmonic response. The study showed the effect of the pendulum length variability on the whole system’s performance. The vertically excited parametric pendulum with variable length in the system is established, giving faster and longer oscillations than the pendulum with constant length. Hence, more and richer dynamics are achieved. A quasi-periodicity behavior is noticed in the system even after 50 s of simulation time; this can be compensated when a regular external forcing is applied. Furthermore, the lever and piston oscillations show a transient behavior before it finally reaches a stable behavior.

show abstract

“…To evaluate the dynamic properties of nonlinear systems, a variety of tools may be used. The most effective and the most frequently used are numerical methods that allow estimation of the largest Lyapunov exponent [9], bifurcation diagrams [10], Fast Fourier Transform [11] and Poincare cross-sections [12]. In general terms Lyapunov exponents are defined by means of numerical coefficients, which characterize the increase of the distance measured between trajectories initially located in close proximity, observed on the phase plane.…”

Section: Introductionmentioning

confidence: 99%

Chaos in overhead travelling cranes load motion

Margielewicz

Gąska

Opasiak

et al. 2019

mech

View full text Add to dashboard Cite

The paper presents the results of numerical investigations of the overhead travelling cranes load motion. The model studies assumes that the load is suspended on the inextensible rope. Conversely, its motion is triggered by an external moment. In addition, energy losses in the construction node connecting the rope to the drum are included. At the same time these losses were mapped through a linear viscous damper. The main objective was to evaluate the impact of individual mathematical model parameters on the dynamics of the transported load. The results were compared between two models: with/without crane structure vibrations included. The results were illustrated by multi-colored maps of the largest Lyapunov exponent, bifurcation diagrams, and Poincare cross-sections.

show abstract

Bifurcation study of a chaotic model variable-length pendulum on a vibrating base

Cited by 13 publications

References 18 publications

On the Modeling and Simulation of Variable-Length Pendulum Systems: A Review

On the Modeling and Simulation of Variable-Length Pendulum Systems: A Review

Modeling, Simulation, and Analysis of a Variable-Length Pendulum Water Pump

Chaos in overhead travelling cranes load motion

Contact Info

Product

Resources

About