Special Issue "Fractional Vibrations: Theory and Applications"

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: 31 December 2021.

Special Issue Editors

Prof. Dr. Ming Li
E-Mail Website1 Website2
Guest Editor
Ocean College, Zhejiang University, Hangzhou 310027, Zhejiang, China
Interests: fractal time series; long-range dependent processes; self-similar processes; ocean waves; sea level time series; network traffic
Prof. Dr. Carlo Cattani
E-Mail Website
Guest Editor
Engineering School (DEIM), University of Tuscia, Largo dell'Università, 01100 Viterbo, Italy
Interests: wavelets; fractals; fractional calculus; dynamical systems; data analysis; time series analysis; image analysis; computer science; computational methods; composite materials; elasticity; nonlinear waves
Special Issues and Collections in MDPI journals
Dr. Mohammad Hossein Heydari
E-Mail Website
Guest Editor
Department of Mathematics, Shiraz University of Technology, 71557-13876 Shiraz, Iran
Interests: wavelets theory; fractional calculus; fractional optimal control; stochastic differential equations

Special Issue Information

Dear Colleagues

Fractional vibrations have attracted interest from researchers in various fields, ranging from mechanical engineering to mechanics of materials. The topic of this Special Issue is the Theory and Applications of Fractional Vibrations, and its focus is two-fold: the theory of fractional vibrations, such as the responses and dynamics of fractional vibrators, and applications, such as theoretical explanations of the Rayleigh damping assumption or structure–fluid coupling vibrations.

Specifically, the goal of this Special Issue is to develop the theory and applications of fractional vibrations except conventional nonlinear ones. We are interested in mechanical engineering applications, and recent advances in the theory of fractional vibrations with a mathematics or mechanics approach.

High quality papers, including research articles and reviews, are invited in, among others, the following areas:

  • Theory and applications of fractional vibrations.
  • Fractional multi-degree-of freedom vibrations.
  • Theoretical explanations of the Rayleigh damping assumption.
  • Fractional beams.
  • Fractional wave equations.
  • Fractional Kelvin–Voigt model
  • Fractional vibrations in marine structures.
  • Fractional vibrations in structure–fluid coupling.
  • Fractional vibrations in hydro–elasticity
  • Fractional noise produced by fractional vibration systems.
  • Dynamics of fractional vibrations.

Prof. Dr. Ming Li
Prof. Dr. Carlo Cattani
Dr. Mohammad Hossein Heydari
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (1 paper)

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Research

Article
Vibration Systems with Fractional-Order and Distributed-Order Derivatives Characterizing Viscoinertia
Fractal Fract. 2021, 5(3), 67; https://doi.org/10.3390/fractalfract5030067 - 12 Jul 2021
Viewed by 450
Abstract
We considered forced harmonic vibration systems with the Liouville–Weyl fractional derivative where the order is between 1 and 2 and with a distributed-order derivative where the Liouville–Weyl fractional derivatives are integrated on the interval [1, 2] with respect to the order. Both types [...] Read more.
We considered forced harmonic vibration systems with the Liouville–Weyl fractional derivative where the order is between 1 and 2 and with a distributed-order derivative where the Liouville–Weyl fractional derivatives are integrated on the interval [1, 2] with respect to the order. Both types of derivatives enhance the viscosity and inertia of the system and contribute to damping and mass, respectively. Hence, such types of derivatives characterize the viscoinertia and represent an “inerter-pot” element. For such vibration systems, we derived the equivalent damping and equivalent mass and gave the equivalent integer-order vibration systems. Particularly, for the distributed-order vibration model where the weight function was taken as an exponential function that involved a parameter, we gave detailed analyses for the weight function, the damping contribution, and the mass contribution. Frequency–amplitude curves and frequency-phase curves were plotted for various coefficients and parameters for the comparison of the two types of vibration models. In the distributed-order vibration system, the weight function of the order enables us to simultaneously involve different orders, whilst the fractional-order model has a single order. Thus, the distributed-order vibration model is more general and flexible than the fractional vibration system. Full article
(This article belongs to the Special Issue Fractional Vibrations: Theory and Applications)
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