Modeling and Control in Vibrational and Structural Dynamics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E4: Mathematical Physics".

Deadline for manuscript submissions: 30 September 2025 | Viewed by 379

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Department of Architecture and Civil Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon 852, Hong Kong
Interests: environmental noise; interior acoustic; random vibration; nonlinear structural dynamics; finite element method; smart and composite structures; active noise and structural vibration control; measurement techniques in noise and structural vibration
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Special Issue Information

Dear Colleagues,

This Special Issue aims to examine the new developments in modeling and control in structural dynamics and various solution methods for special vibrational structures. Papers of theoretical and experimental nature are welcome. Acoustic and vibrational properties are commonly inherent in numerous physical and engineering systems, which have been studied by various researchers. Thus, the scope of this Special Issue is very wide. It includes papers on dynamic modeling and vibration of structural elements. Adaptive computational methods, linear/nonlinear dynamic behaviors of smart structures/materials, dynamic stability of discrete and continuous systems, application of numerical techniques in studying linear/nonlinear dynamics of beams, arches, cables, plates, and shells; dynamic systems involving clearances, impacts, and friction; dynamics of micro-scale systems; linear/nonlinear behaviors of soil-structure, structural-acoustic, and fluid-structural interactions, stability and bifurcation analysis of piecewise systems and structures, dynamic response of hysteretic systems; vibration absorbers; rotor dynamics of systems; applications of smart sensors and actuators; multi-objective optimization. Experimental studies, which verify theoretical results, are also of particular interest.

Dr. Yiu Yin Raymond Lee
Guest Editor

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Keywords

  • modeling and control in vibrational and structural dynamics
  • active sound and vibration control
  • classical/numerical methods for studying dynamic systems
  • soil–structure, structural–acoustic, and fluid–structural interactions
  • stability and bifurcation analyses
  • linear/nonlinear beams, arches, cables, plates, and shells
  • active and passive control
  • sensor and actuator
  • experimental studies and measurement techniques
  • vibration isolation
  • optimization for a structural problem
  • harmonic balance method, perturbation method, method of multiple scales
  • nonlinear oscillator

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Published Papers (1 paper)

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Research

17 pages, 2089 KiB  
Article
Analytical Periodic Solutions for Non-Homogenous Integrable Dispersionless Equations Using a Modified Harmonic Balance Method
by Muhammad Irfan Khan, Yiu-Yin Lee and Muhammad Danish Zia
Mathematics 2025, 13(15), 2386; https://doi.org/10.3390/math13152386 - 24 Jul 2025
Viewed by 187
Abstract
In this study, we outline a modified harmonic balance method for solving non-homogenous integrable dispersionless equations and obtaining the corresponding periodic solutions, a research field which shows limited investigation. This study is the first to solve this nonlinear problem, based on a recently [...] Read more.
In this study, we outline a modified harmonic balance method for solving non-homogenous integrable dispersionless equations and obtaining the corresponding periodic solutions, a research field which shows limited investigation. This study is the first to solve this nonlinear problem, based on a recently developed harmonic balance method combined with Vieta’s substitution technique. A set of analytical formulas are generated from the modified harmonic balance method and used to compute the approximate periodic solutions of the dispersionless equations. The main advantage of this method is that the computation effort required in the solution procedure can be smaller. The results of the modified harmonic balance method show reasonable agreement with those obtained using the classic harmonic balance method. Our proposed solution method can decouple the nonlinear algebraic equations generated in the harmonic balance process. We also investigated the effects of various parameters on nonlinear periodic responses and harmonic convergence. Full article
(This article belongs to the Special Issue Modeling and Control in Vibrational and Structural Dynamics)
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