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Mathematics
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Advanced Modeling and Design of Vibration and Wave Systems
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Advanced Modeling and Design of Vibration and Wave Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 20 July 2026 | Viewed by 9364

Special Issue Editors

Dr. Soo-Ho Jo

E-Mail Website
Guest Editor
Department of Mechanical, Robotics, and Energy Engineering, Dongguk University, Seoul 04620, Republic of Korea
Interests: metastructure; piezoelectric; sensors; actuators; artificial intelligence
Special Issues, Collections and Topics in MDPI journals
Dr. Haichao An

E-Mail Website
Guest Editor
School of Aerospace Science and Technology, Beijing Institute of Technology, Beijing, China
Interests: flight vehicle structural analysis; structural design optimization; composite structure design
Special Issues, Collections and Topics in MDPI journals
Dr. Jaehun Lee

E-Mail Website
Guest Editor
Department of Mechanical, Robotics, and Energy Engineering, Dongguk University, Seoul 04620, Republic of Korea
Interests: reduced-order modeling; AI-based design and analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue seeks to explore state-of-the-art methodologies in the modeling and design of vibration and wave systems. Such methodologies include analytical, numerical, data-driven, and physics-informed AI approaches. Vibration and wave engineering are critical in various fields, including mechanics, acoustics, materials science, and others. This Special Issue aims to showcase advancements that enhance our understanding of these systems. These advancements will address challenges such as multi-physics and/or multi-scale interactions, nonlinear problems, and complex geometries.

We encourage the submission of contributions that concentrate on innovative modeling techniques for vibration and wave analysis and design optimization strategies intended to enhance output performance. The interdisciplinary nature of this Special Issue invites submissions that connect theoretical developments with practical applications, thereby fostering a deeper integration of advanced modeling with real-world engineering solutions.

By fostering collaboration between researchers from diverse backgrounds, this Special Issue aims to accelerate the development of next-generation technologies for the improved design of vibration and wave systems.

Dr. Soo-Ho Jo
Dr. Haichao An
Dr. Jaehun Lee
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 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 250 words) can be sent to the Editorial Office for assessment.

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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 dynamics
  • multi-scale interactions
  • multi-physics systems
  • metastructures
  • phononic crystals
  • data-driven modeling
  • advanced analytical modeling
  • advanced numerical modeling
  • design optimization
  • physics-informed AI
  • AI-driven inverse design

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Published Papers (7 papers)

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Research

37 pages, 9096 KB  
Article
A Numerical Study of Tunable Multifunctional Metastructures via Solid–Liquid Phase Transition for Simultaneous Control of Sound and Vibration
by Hyeonjun Jeong and Jaeyub Hyun
Mathematics 2026, 14(7), 1213; https://doi.org/10.3390/math14071213 - 4 Apr 2026
Viewed by 252
Abstract
Metastructures, waveguides composed of multiple unit cells (meta-atoms), have gained significant attention for controlling wave propagation in engineering applications, especially in the context of elastic and acoustic waves. However, existing metastructures often lack sufficient tunable functionality to dynamically control both elastic vibration and [...] Read more.
Metastructures, waveguides composed of multiple unit cells (meta-atoms), have gained significant attention for controlling wave propagation in engineering applications, especially in the context of elastic and acoustic waves. However, existing metastructures often lack sufficient tunable functionality to dynamically control both elastic vibration and acoustic wave transmission using a single external parameter. This study introduces a phase-change material (PCM)-embedded meta-atom, where a core mass is connected to an outer shell by Archimedean spiral bridges. The solid–liquid phase transition of PCM induces a notable change in the effective shear modulus, enabling dynamic wave control. The mechanism for bandgap formation transitions from Bragg scattering in the solid PCM state to local resonance in the liquid state. Core rotation, driven by the phase transition, is key to generating flat bands and low-frequency locally resonant bandgaps at high temperatures. Temperature-dependent, mode-selective transmission behavior is observed, with transverse vibrations and acoustic waves exhibiting opposite blocking and transmission characteristics at the same frequency. This design provides a promising approach for decoupling sound and vibration management, using temperature control driven by the PCM phase transition. The work contributes to multifunctional metastructures with applications in adaptive noise control, structural health monitoring, and tunable vibration isolation systems. Full article
(This article belongs to the Special Issue Advanced Modeling and Design of Vibration and Wave Systems)
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18 pages, 2924 KB  
Article
Double Fourier Series-Based Sideband Harmonic Analysis of a Full-Bridge Converter
by Junhyeok Choi and Yeongsu Bak
Mathematics 2026, 14(4), 617; https://doi.org/10.3390/math14040617 - 10 Feb 2026
Viewed by 442
Abstract
To respond to carbon-neutrality policies, interest in transportation powered by eco-friendly energy has increased. These systems require high-efficiency power conversion stages that enable bidirectional operation for driving and regenerative braking, where full-bridge converter topologies are widely adopted. However, harmonics in full-bridge converters can [...] Read more.
To respond to carbon-neutrality policies, interest in transportation powered by eco-friendly energy has increased. These systems require high-efficiency power conversion stages that enable bidirectional operation for driving and regenerative braking, where full-bridge converter topologies are widely adopted. However, harmonics in full-bridge converters can degrade efficiency and power density and cause electromagnetic compatibility issues. Therefore, the harmonic frequency bands and amplitudes must be accurately predicted. A single-variable Fourier series can estimate the baseband and carrier harmonics. However, the fundamental frequency of motor drive systems and railway vehicles generates the sideband harmonic which is determined by the baseband and carrier harmonics. Therefore, accurately predicting the sideband harmonics is difficult when using a single-variable Fourier series. This paper proposes a double Fourier series (DFS)-based sideband harmonic analysis of a full-bridge converter. To validate the applicability of the proposed method to various full-bridge based systems, four sets of results are compared over multiple combinations of the fundamental and carrier frequencies, including DFS without deadtime, DFS with deadtime, simulation results, and experimental results. Full article
(This article belongs to the Special Issue Advanced Modeling and Design of Vibration and Wave Systems)
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16 pages, 6542 KB  
Article
Transient Response Enhancement of PMD Battery Charger Using Rule-Based Fuzzy Logic Control
by Gijeong Yoon and Yeongsu Bak
Mathematics 2026, 14(4), 585; https://doi.org/10.3390/math14040585 - 7 Feb 2026
Viewed by 273
Abstract
This paper proposes a transient response enhancement of a personal mobility device (PMD) battery charger using a rule-based fuzzy logic control (RBFLC) method. PMD encompasses various applications, including electric kickboards, electric scooters, and electric wheelchairs. The rated battery voltage required for each device [...] Read more.
This paper proposes a transient response enhancement of a personal mobility device (PMD) battery charger using a rule-based fuzzy logic control (RBFLC) method. PMD encompasses various applications, including electric kickboards, electric scooters, and electric wheelchairs. The rated battery voltage required for each device is different; additionally, the PMD battery charger must be accurate and have a fast transient response. However, when the gain is significantly increased in the conventional proportional-integral (PI) control method to enhance the transient response, the battery charger output voltage exhibits oscillatory behavior and becomes unstable. Therefore, in this paper, the RBFLC method is proposed to improve the transient response performance of the battery charger without oscillation and instability of the output voltage. The proposed RBFLC method is verified through simulation and experimental results. Full article
(This article belongs to the Special Issue Advanced Modeling and Design of Vibration and Wave Systems)
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17 pages, 2180 KB  
Article
Multi-Objective Optimization of Design Parameters to Improve Dynamic Performances of Distributed Actuation Mechanism
by Ik Hyun Jo and Jong Ho Kim
Mathematics 2025, 13(23), 3773; https://doi.org/10.3390/math13233773 - 24 Nov 2025
Viewed by 483
Abstract
The distributed actuation mechanism (DAM) is inspired by the motion of biological muscles and enables efficient modulation between speed and force through a variable gearing concept. This study proposes an advanced modeling-based multi-objective optimization framework that enhances the dynamic performance of a DAM-based [...] Read more.
The distributed actuation mechanism (DAM) is inspired by the motion of biological muscles and enables efficient modulation between speed and force through a variable gearing concept. This study proposes an advanced modeling-based multi-objective optimization framework that enhances the dynamic performance of a DAM-based manipulator by simultaneously improving its end-effector velocity and payload capacity. The kinematic and dynamic characteristics of the DAM are mathematically modeled to capture the interactions among design parameters, and a high-fidelity multibody dynamics model is developed using RecurDyn. Then, a sequential quadratic programming (SQP) algorithm implemented in MATLAB is employed to perform optimization under geometric and physical constraints. The results demonstrate that the proposed optimization method achieved increases of approximately 46.5% in maximum velocity and over 40% in maximum payload, confirming the effectiveness of the advanced modeling-based optimization strategy. It was also found that link-length ratios and hinge offsets play critical roles in determining the DAM’s dynamic behavior. The proposed framework provides a systematic and practical approach for integrating mathematical modeling with design optimization and offers valuable guidelines for improving the structural design and performance of distributed-actuation-based robotic manipulators. Full article
(This article belongs to the Special Issue Advanced Modeling and Design of Vibration and Wave Systems)
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22 pages, 5924 KB  
Article
Topology Optimization of Automotive Vibration Test Jig: Natural Frequency Maximization and Weight Reduction
by Jun Won Choi, Min Gyu Kim, Jung Jin Kim and Jisun Kim
Mathematics 2025, 13(11), 1716; https://doi.org/10.3390/math13111716 - 23 May 2025
Cited by 1 | Viewed by 1922
Abstract
Vibration test jigs are essential components for evaluating the dynamic performance and durability of automotive parts, such as lamps. This study aimed to derive optimal jig configurations that simultaneously maximize natural frequency and minimize structural weight through topology optimization. A fixed-grid finite-element model [...] Read more.
Vibration test jigs are essential components for evaluating the dynamic performance and durability of automotive parts, such as lamps. This study aimed to derive optimal jig configurations that simultaneously maximize natural frequency and minimize structural weight through topology optimization. A fixed-grid finite-element model was constructed by incorporating realistic lamp mass and boundary conditions at the mounting interfaces to simulate actual testing scenarios. Four optimization formalizations were investigated: (1) compliance minimization, (2) compliance minimization with natural-frequency constraints, (3) natural-frequency maximization, and (4) natural-frequency maximization with compliance constraints. Both full-domain and reduced-domain designs were analyzed to assess the influence of domain scope. The results indicate that formulations that use only natural-frequency objectives often result in shape divergence and convergence instability. In contrast, strategies incorporating frequency as a constraint—particularly compliance minimization with a natural-frequency constraint—exhibited superior performance by achieving a balance between stiffness and weight. Furthermore, the reduced-domain configuration enhanced the natural frequency owing to the greater design freedom, although this resulted in a trade-off of increased weight. These findings underscore the importance of selecting appropriate formalization strategies and domain settings to secure reliable vibration performance and support the necessity of multi-objective optimization frameworks for the practical design of vibration-sensitive structures. Full article
(This article belongs to the Special Issue Advanced Modeling and Design of Vibration and Wave Systems)
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19 pages, 38387 KB  
Article
Vibration Reduction of Permanent Magnet Synchronous Motors by Four-Layer Winding: Mathematical Modeling and Experimental Validation
by Young-Hoon Jung, Dong-Min Kim, Kyoung-Soo Cha, Soo-Hwan Park and Min-Ro Park
Mathematics 2025, 13(10), 1603; https://doi.org/10.3390/math13101603 - 13 May 2025
Cited by 2 | Viewed by 1723
Abstract
This paper proposes a vibration reduction method for fractional slot concentrated winding (FSCW) permanent magnet synchronous motors (PMSMs) by applying a four-layer winding configuration. The radial electromagnetic force (REF), particularly its low space-harmonics, causes significant vibration in PMSMs. These low-order REF components are [...] Read more.
This paper proposes a vibration reduction method for fractional slot concentrated winding (FSCW) permanent magnet synchronous motors (PMSMs) by applying a four-layer winding configuration. The radial electromagnetic force (REF), particularly its low space-harmonics, causes significant vibration in PMSMs. These low-order REF components are influenced by sub-harmonics in the airgap magnetic flux density (MFD), which occur at frequencies lower than the fundamental component generated by the armature magnetomotive force (MMF) in FSCW PMSMs. To mitigate these sub-harmonics in the MFD, the four-layer winding is applied to the FSCW PMSM. As a result, the overall vibration of the motor is reduced. To verify the effectiveness of the four-layer winding, both electrical and mechanical characteristics are compared among motors with conventional one-, two-, and, proposed, four-layer windings. Finally, the three motors are fabricated and tested, and their vibration levels are experimentally evaluated. Full article
(This article belongs to the Special Issue Advanced Modeling and Design of Vibration and Wave Systems)
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19 pages, 5504 KB  
Article
Progressive Domain Decomposition for Efficient Training of Physics-Informed Neural Network
by Dawei Luo, Soo-Ho Jo and Taejin Kim
Mathematics 2025, 13(9), 1515; https://doi.org/10.3390/math13091515 - 4 May 2025
Cited by 4 | Viewed by 3333
Abstract
This study proposes a strategy for decomposing the computational domain to solve differential equations using physics-informed neural networks (PINNs) and progressively saving the trained model in each subdomain. The proposed progressive domain decomposition (PDD) method segments the domain based on the dynamics of [...] Read more.
This study proposes a strategy for decomposing the computational domain to solve differential equations using physics-informed neural networks (PINNs) and progressively saving the trained model in each subdomain. The proposed progressive domain decomposition (PDD) method segments the domain based on the dynamics of residual loss, thereby indicating the complexity of different sections within the entire domain. By analyzing residual loss pointwise and aggregating it over specific intervals, we identify critical regions requiring focused attention. This strategic segmentation allows for the application of tailored neural networks in identified subdomains, each characterized by varying levels of complexity. Additionally, the proposed method trains and saves the model progressively based on performance metrics, thereby conserving computational resources in sections where satisfactory results are achieved during the training process. The effectiveness of PDD is demonstrated through its application to complex PDEs, where it significantly enhances accuracy and conserves computational power by strategically simplifying the computational tasks into manageable segments. Full article
(This article belongs to the Special Issue Advanced Modeling and Design of Vibration and Wave Systems)
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