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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 November 2025 | Viewed by 774

Special Issue Editors

Dr. Soo-Ho Jo

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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
Guest Editor
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
Interests: structural optimization; composite structure optimization; optimal sensor placement
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
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 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. 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 (2 papers)

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19 pages, 38387 KiB  
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
Viewed by 212
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 KiB  
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
Viewed by 332
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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