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Symmetry
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Symmetry in Modeling and Analysis of Dynamic Systems II
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Symmetry in Modeling and Analysis of Dynamic Systems II

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

Deadline for manuscript submissions: closed (15 October 2022) | Viewed by 2731

Special Issue Editor

Prof. Dr. Jan Awrejcewicz

E-Mail Website
Guest Editor
Faculty of Mechanical Engineering, Lodz University of Technology, 90-924 Łódź, Poland
Interests: nonlinear dynamics; non-linear mechanics; control; biomechanics; mechatronics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is the continuation of the previous one recently published in Symmetry.

The proposed Special Issue (SI) of the journal Symmetry aims to cover the exchange and dissemination of the concept of symmetry in the modeling and analysis of dynamic features occurring in various branches of science including physics, chemistry, biology, and engineering (mechanics, mechatronics, civil engineering, electronics, informatics, bioengineering, etc.).

The approaches based on dynamical symmetry breaking generalize and unify theories developed and employed in the aforementioned sciences under the concept of invariance of the global/local behavior of the points of spacetime, including temporal/spatiotemporal symmetries.

Since a property of the symmetry of the investigated system implies its conservation quantity like energy, linear/angular momentum, electric charge etc., contributions of research based on the mathematical models of nonlinear partial and ordinary differential equations are especially welcome.

The following topics are also included: (i) discrete vs. continuous symmetry breaking; (ii) solitary waves; (iii) symmetry breaking instability; (iv) symmetry exhibited by MEMS/NEMS; (v) arrays of oscillators subjected to electric/magnetic/thermal fields; (vi) time-symmetry breaking in quantum oscillators; (vii) symmetry breaking of resonances; (viii) symmetry in fluid-structure interaction; (ix) symmetry vs. asymmetry in pattern formation; (x) symmetry in solid-gas phase transition; (xi) continuous vs. discontinuous symmetry; (xii) temporal vs. spatiotemporal symmetry; (xiii) symmetry in transition from regular to chaotic dynamics.

Prof. Dr. Jan Awrejcewicz
Guest Editor

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 submissions that pass pre-check are 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. Symmetry is an international peer-reviewed open access monthly 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 2400 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.

Keywords

  • nonlinear ODES and PDEs
  • stability
  • bifurcation
  • chaos
  • resonance
  • boundary conditions

Published Papers (2 papers)

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Research

15 pages, 969 KiB  
Article
Surface Waves on a Coated Homogeneous Half-Space under the Effects of External Forces
by Ali M. Mubaraki and Fadhel M. Almalki
Symmetry 2022, 14(11), 2241; https://doi.org/10.3390/sym14112241 - 25 Oct 2022
Cited by 2 | Viewed by 1011
Abstract
The present study focuses on the examination of the propagation of plane surface waves on a coated half-space, which is accompanied by the magnetic field force, and the normal mechanical loading, due to Winkler’s elastic foundation. The study is based upon the application [...] Read more.
The present study focuses on the examination of the propagation of plane surface waves on a coated half-space, which is accompanied by the magnetic field force, and the normal mechanical loading, due to Winkler’s elastic foundation. The study is based upon the application of the analytical and asymptotic integration procedures to acquire and further analyze the aspiring secular equation. Asymptotically, the influence of the coating layer is suppressed by deploying apposite effective boundary conditions that are ingrained on a long-wave approximation condition, to obtain the resulting pseudo-differential operator of the reduced equation of surface motion. In fact, the comparison between the two approaches yielded considerable agreement through the dependency plots, featuring the scaled velocity v/vR versus the dimensionless wavenumber K. Moreover, certain well-known results in the literature are obtained as liming circumstances of the present examination. Additionally, an insightful finding about the vanishing possibility of the coating layer is illustratively highlighted. Full article
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems II)
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23 pages, 613 KiB  
Article
Two New Models for Dynamic Linear Elastic Beams and Simplifications for Double Symmetric Cross-Sections
by Erick Pruchnicki
Symmetry 2022, 14(6), 1093; https://doi.org/10.3390/sym14061093 - 26 May 2022
Cited by 2 | Viewed by 1230
Abstract
We present two new models for dynamic beams deduced from three dimensional theory of linear elasticity. The first model is deduced from virtual work considered for small beam sections. For the second model, we suppose a Taylor-Young expansion of the displacement field up [...] Read more.
We present two new models for dynamic beams deduced from three dimensional theory of linear elasticity. The first model is deduced from virtual work considered for small beam sections. For the second model, we suppose a Taylor-Young expansion of the displacement field up to the fourth order in transverse dimensions of the beam. We consider the Fourier series expansion for considering Neumann lateral boundary conditions together with dynamical equations, we obtain a system of fifteen vector equations with the fifteen coefficients vector unknown of the displacement field. For beams with two fold symmetric cross sections commonly used (for example circular, square, rectangular, elliptical…), a unique decomposition of any three-dimensional loads is proposed and the symmetries of these loads is introduced. For these two theories, we show that the initial problem decouples into four subproblems. For an orthotropic material, these four subproblems are completely independent. For a monoclinic material, two subproblems are coupled and independent of the two other coupled subproblems. For the first model, we also give the detailed expression of these four subproblems when we consider the approximation of the displacement field used in the second model. Full article
(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems II)
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