Interdisciplinary Applications of Dynamical Systems

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (19 December 2024) | Viewed by 847

Special Issue Editor


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Guest Editor
Department of Mathematics, Hampton University, 246B Science and Technology Hall, 609 Norma B Harvey Road, Hampton, VA 23669, USA
Interests: dynamical systems theory and applications; theory and applications of nonlinear dynamics and chaos and their integration with data-driven methods; engineering mechanics; chemical reactions; magnetic confinement of plasma

Special Issue Information

Dear Colleagues,

All systems in physical sciences and engineering can be modeled as dynamical systems, and techniques such as stability of equilibria, trajectory, bifurcation and Poincaré section are ubiquitous in analyzing nonlinear systems. The focus of this Special Issue is to collect recent advances in modern applied dynamical systems to mathematical physics, chemistry, biology and engineering. The specific applications will include, but are not limited to, celestial mechanics, solid mechanics, chemical reactions, fluid mechanics, magnetic confinement of plasma, neural dynamics and complex networks from a mathematical viewpoint. We invite articles on applications where the dynamical system viewpoint has led to new insights and the study shows an improved modeling and control of dynamical behavior. We also invite articles on the dynamical system viewpoint of data-driven systems which are modeled using observation and simulation data, and where new dynamical system techniques were developed for a specific class of systems.

Dr. Shibabrat Naik
Guest Editor

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Keywords

  • nonlinear dynamics
  • dynamical system theory
  • ODEs, PDEs, DDEs
  • periodic orbits
  • invariant manifolds
  • stability analysis
  • system identification
  • global bifurcation and chaos
  • geometric view of dynamics
  • applied dynamical systems

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Published Papers (1 paper)

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Research

20 pages, 6001 KiB  
Article
Structure-Borne Sound Suppression of a Strongly/Weakly Excited Curved Panel Using a Quadratic Nonlinear Resonance Effect
by Yiu-Yin Lee
Axioms 2025, 14(2), 125; https://doi.org/10.3390/axioms14020125 - 9 Feb 2025
Viewed by 558
Abstract
This study aimed to investigate the structure-borne sound suppression of a strongly/weakly excited curved panel. Quadratic nonlinear resonance can induce anti-symmetric modal responses to replace symmetric modal responses, even though the physical panel dimensions and excitation distribution are symmetric. Unlike cubic nonlinear resonance, [...] Read more.
This study aimed to investigate the structure-borne sound suppression of a strongly/weakly excited curved panel. Quadratic nonlinear resonance can induce anti-symmetric modal responses to replace symmetric modal responses, even though the physical panel dimensions and excitation distribution are symmetric. Unlike cubic nonlinear resonance, quadratic nonlinear resonance can be induced regardless of whether the panel vibration amplitude is small or large. As the sound radiation efficiency of anti-symmetric responses is much lower than that of symmetric responses, this quadratic nonlinear resonance effect is thus used for sound suppression. A set of multimode formulations was developed from the nonlinear structural governing equation and sound radiation efficiency equation. The quadratic nonlinear resonant responses and some other nonlinear responses were computed from the multimode formulations. Modal convergence studies and parametric studies were performed to understand the effects of various parameters on the quadratic nonlinear responses and sound suppression. The results showed that when the panel was strongly excited, the difference between the peak sound levels in the linear and nonlinear cases was up to 12 dB, and when the panel was weakly excited, the difference was up to 6 dB. Full article
(This article belongs to the Special Issue Interdisciplinary Applications of Dynamical Systems)
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