Nonlinear Vibrations and Chaos: Symmetry and Topics of Symmetry

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Engineering and Materials".

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 1851

Special Issue Editor


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Guest Editor
School of Science, Engineering, and Technology, Penn State Harrisburg, 777 West Harrisburg Pike, W-255 Olmsted Building, Middletown, PA 17057, USA
Interests: nonlinear vibrations and chaos; machine learning and AI; manufacturing processes; monitoring; optimization and reliability; machinery sound and noise control

Special Issue Information

Dear Colleagues,

Nonlinear structural and mechanical systems are known to exhibit extensively rich and complex motion patterns. Such a diverse vibrational response is characterized by the presence of bifurcations, multiple coexisting modes, period doubling, and chaos. It is also documented that some manufacturing processes—for example, metal cutting—exhibit nonlinear vibrations that may include unpredictable chaotic behavior. Nonlinear and chaotic vibrations are usually described using tools such as iterated maps, phase plane analysis, Poincaré sections, bifurcation diagrams, fractal dimension, statistical parameters, and time–frequency wavelet analysis. Understanding the correlation between the patterns of symmetry in the vibration response and system parameters is fundamental to predicting and controlling these nonlinear systems. This Special Issue emphasizes the implications of symmetry and asymmetry of nonlinear vibrations and chaotic motion and the consideration of symmetry in structural properties that influence system response. Referring to nonlinear vibrations and chaos, this Special Issue welcomes novel research papers and comprehensive reviews dealing with recent theoretical and experimental developments within the scope of this journal.

Prof. Dr. Issam Abu-Mahfouz
Guest Editor

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Keywords

  • applications of nonlinear vibrations and chaos
  • bifurcation and period doubling
  • chaos and chaotic motion
  • fractals
  • nonlinear vibrations
  • poincare’ section
  • strange attractor
  • symmetry in chaotic vibrations

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Published Papers (1 paper)

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Research

19 pages, 15543 KiB  
Article
Symmetry and Asymmetry of Chaotic Motion in a Crank Arm and Connecting Rod Due to the Movement of the Follower
by Louay S. Yousuf
Symmetry 2023, 15(12), 2148; https://doi.org/10.3390/sym15122148 - 3 Dec 2023
Viewed by 1030
Abstract
The symmetry and asymmetry of chaotic motion in the planar mechanism is investigated for a crank arm and connecting rod due to the motion of a flat-faced follower. The level of chaos is investigated using the conception of the Lyapunov exponent parameter and [...] Read more.
The symmetry and asymmetry of chaotic motion in the planar mechanism is investigated for a crank arm and connecting rod due to the motion of a flat-faced follower. The level of chaos is investigated using the conception of the Lyapunov exponent parameter and phase-plane diagram at different cam speeds with and without the use of coefficients of restitution. Moreover, the fast Fourier transform (FFT) of power spectrum analysis technique is used based on SNR factor values at different cam speeds and different coefficients of restitution. The wave forms and histograms of nonlinear responses are analyzed using the SolidWorks program for the crank arm, connecting rod, and flat-faced follower. There is a clearance between the flat-faced follower and its guides while the oscillation motion of the crank arm and connecting rod is described as the motion of a double pendulum. The level of chaos is increased with increases in the cam speeds and coefficients of restitution. Full article
(This article belongs to the Special Issue Nonlinear Vibrations and Chaos: Symmetry and Topics of Symmetry)
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