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Nonlinear Dynamics and Vibration
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Nonlinear Dynamics and Vibration

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Acoustics and Vibrations".

Deadline for manuscript submissions: 20 August 2025 | Viewed by 4575

Special Issue Editors

Dr. Giovanni Iarriccio

E-Mail Website
Guest Editor
Department of Engineering “Enzo Ferrari”, University of Modena and Reggio Emilia, 41125 Modena, Italy
Interests: applied mechanics; nonlinear dynamics; vibrations; structural mechanics; NVH; machine theory; vehicle dynamics
Dr. Matteo Strozzi

E-Mail Website
Guest Editor
Department of Sciences and Methods for Engineering, University of Modena and Reggio Emilia, 42122 Reggio Emilia, Italy
Interests: nonlinear vibrations; energy exchange in dynamics; applied mechanics; nanotubes; FGM
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

While linear models are often effective, the physics of our world is governed by nonlinear equations. Bridging the gap between theory and practice is crucial for understanding and improving the performance and reliability of modern engineering systems.

This Special Issue of Applied Sciences aims to present the latest advances and research findings in nonlinear dynamics and vibration. It combines theoretical, experimental, and computational contributions that enhance our understanding of complex dynamic behavior in various engineering applications.

Research articles, review papers, and case studies that address fundamental aspects and practical applications of nonlinear dynamics and vibration are welcome. Contributions that offer new insights on physical systems, explore innovative methodologies, and have emerging applications are particularly encouraged.

Topics of interest for this Special Issue include, but are not limited to, the following:

  • Tuning nonlinearities for optimal performance;
  • Internal and parametric resonances;
  • Self-excited oscillations;
  • Energy transfer and localization phenomena;
  • Bifurcation and stability phenomena;
  • Reduced-order models;
  • Experimental observation of nonlinear phenomena.

Dr. Giovanni Iarriccio
Dr. Matteo Strozzi
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. Applied Sciences 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 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 dynamics
  • vibrations
  • bifurcation
  • stability
  • nonlinear interaction
  • continuous systems
  • multi-degree of freedom systems
  • periodic structures
  • experimental methods

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Published Papers (5 papers)

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Research

16 pages, 5766 KiB  
Article
Primary Resonance Analysis of High-Static–Low-Dynamic Stiffness Isolators with Piecewise Stiffness, Viscous Damping, and Dry Friction
by Giovanni Iarriccio
Appl. Sci. 2025, 15(8), 4187; https://doi.org/10.3390/app15084187 - 10 Apr 2025
Viewed by 242
Abstract
High-Static–Low-Dynamic Stiffness (HSLDS) isolators have been extensively studied, primarily considering continuous stiffness and viscous damping, often overlooking stiffness discontinuities and dry friction forces. This paper aims to provide a more accurate model of real systems by investigating the dynamic behavior of HSLDS isolators, [...] Read more.
High-Static–Low-Dynamic Stiffness (HSLDS) isolators have been extensively studied, primarily considering continuous stiffness and viscous damping, often overlooking stiffness discontinuities and dry friction forces. This paper aims to provide a more accurate model of real systems by investigating the dynamic behavior of HSLDS isolators, including piecewise nonlinear–linear stiffness, viscous damping, and dry friction. The equation of motion is analyzed using the Krylov–Bogoliubov–Mitropolsky (KBM) averaging method, deriving approximate analytical expressions to evaluate the frequency response curves and stability boundaries near primary resonance conditions. The model is validated by comparing the approximate solution with direct numerical integration and Den Hartog’s closed-form solution. A parametric analysis explores the impact of key parameters through amplitude–frequency diagrams and critical forcing boundaries. A numerical example is presented, demonstrating how the present method can be used to identify critical dynamic conditions, such as saddle-node bifurcations and activation of the piecewise restoring force nonlinearity. Results confirm the reliability of the KBM method in dealing with piecewise restoring forces while highlighting its limitations in case of high dry friction. This study offers an approximate yet effective approach for evaluating the system’s dynamic behavior, providing insights that could facilitate the design of isolation mounts and serve as benchmarks for future research. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Vibration)
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16 pages, 4129 KiB  
Article
Nonlinear Dynamics of a Piezoelectric Bistable Energy Harvester Using the Finite Element Method
by Virgilio J. Caetano and Marcelo A. Savi
Appl. Sci. 2025, 15(4), 1990; https://doi.org/10.3390/app15041990 - 14 Feb 2025
Viewed by 515
Abstract
The conversion of ambient mechanical vibrational energy into electrical energy through piezoelectric devices has received an increasing attention in recent years. The main challenges are to develop efficient devices that operate over a wide frequency range, adapting to diverse environmental energy sources. This [...] Read more.
The conversion of ambient mechanical vibrational energy into electrical energy through piezoelectric devices has received an increasing attention in recent years. The main challenges are to develop efficient devices that operate over a wide frequency range, adapting to diverse environmental energy sources. This work presents a framework for the analysis of a nonlinear vibration-based energy harvesting devices combining the nonlinear finite element method with a reduced-order model, which provides a broader dynamical investigation. On this basis, a flexible tool is developed, allowing the multimodal analysis of nonlinear systems. A bistable piezoelectric energy harvesting device is investigated considering the influence of multimodal and nonlinear effects on the system performance. Bistability is due to magnetic interactions among magnets and the beam tip, modeled by cubic nonlinearities. Numerical simulations show the influence of vibration sources on the dynamics and performance of the device. Nonlinear effects furnish rich dynamics, presenting periodic and chaotic responses. All these effects can be combined to enhance energy harvesting capacity. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Vibration)
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24 pages, 6697 KiB  
Article
Recurrence Quantification Analysis (RQA) of Toroidal End Tool Milling Process
by Lukasz Zylka, Marcin Plodzien, Jaroslaw Latalski, Pawel Lajmert and Rafal Rusinek
Appl. Sci. 2025, 15(3), 1347; https://doi.org/10.3390/app15031347 - 28 Jan 2025
Viewed by 731
Abstract
One type of milling process is the face milling of flat surfaces using a toroidal face cutter. A key feature of this process is that changes in the depth of the cut alter the entering angle, impacting milling dynamics by shifting cutting force [...] Read more.
One type of milling process is the face milling of flat surfaces using a toroidal face cutter. A key feature of this process is that changes in the depth of the cut alter the entering angle, impacting milling dynamics by shifting cutting force proportions. To investigate this phenomenon, an experimental study was conducted on the face milling process using different sets of cutting parameters. Cutting force components were recorded, as these signals provide essential information about the milling process. Statistical indicators were then calculated and analyzed based on the recorded data. Following this, a recursive force analysis was performed, and Recurrence Quantification Analysis (RQA) indicators were computed. Relationships between the RQA indicators and the cutting parameters, specifically the feed per tooth (fz) and axial depth of the cut (ap), were established using response surface methodology. Empirical relationships between these parameters were derived. The results indicate that the RQA indicators like the determinism DET, the entropy ENT, and the length of longest vertical line VMAX are correlated with the cutting parameters for both the feed force (Ff) and the component normal to the feed (FfN). In the axial direction, the RQA indicators DET, ENT, and VMAX and also the percentage of recurrence points in a recurrence plot RR and the longest diagonal line length LMAX are shown to be relevant for analyzing the dynamics of the face milling process. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Vibration)
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26 pages, 6967 KiB  
Article
An Efficient Systematic Methodology for Noise and Vibration Analysis of a Reconfigurable Dynamic System Using Receptance Coupling Formulation
by Behzad Hamedi and Saied Taheri
Appl. Sci. 2024, 14(23), 11166; https://doi.org/10.3390/app142311166 - 29 Nov 2024
Cited by 1 | Viewed by 995
Abstract
This study presents a generalized and systematic approach to modeling complex dynamic systems using Frequency-Based Substructuring (FBS). The aim is to develop an efficient method for system identification and subsystem decomposition, enabling the creation of reduced-order models for non-linear dynamic systems that are [...] Read more.
This study presents a generalized and systematic approach to modeling complex dynamic systems using Frequency-Based Substructuring (FBS). The aim is to develop an efficient method for system identification and subsystem decomposition, enabling the creation of reduced-order models for non-linear dynamic systems that are modular and reconfigurable. The methodology combines receptance (Frequency Response Function, FRF) properties from individual subsystems to predict the overall system’s response. This technique extends existing methods by Jetmundsen and D.D. Klerk and adapts them to subsystems with full degrees of freedom (DoFs), making it suitable for flexible and distributed structures. To demonstrate its effectiveness, the method is applied to vehicle noise and vibration analysis, where subsystems are initially treated as rigid bodies, but are later adapted to flexible characteristics. The results show that this hybrid approach accurately predicts system responses, offering significant advantages for NVH target setting when subsystem FRF matrices are sourced either from testing or numerical simulations. This methodology enhances the capability to model complex dynamic systems with improved precision and reduced computational cost. A comparison with traditional modeling techniques confirms the validity of the approach. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Vibration)
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23 pages, 4054 KiB  
Article
Reduced-Order Modeling for Dynamic System Identification with Lumped and Distributed Parameters via Receptance Coupling Using Frequency-Based Substructuring (FBS)
by Behzad Hamedi and Saied Taheri
Appl. Sci. 2024, 14(20), 9550; https://doi.org/10.3390/app14209550 - 19 Oct 2024
Cited by 3 | Viewed by 1284
Abstract
Paper presents an effective technique for developing reduced-order models to predict the dynamic responses of systems using the receptance coupling and frequency-based substructuring (RCFBS) method. The proposed approach is particularly suited for reconfigurable dynamic systems across various applications, like cars, robots, mechanical machineries, [...] Read more.
Paper presents an effective technique for developing reduced-order models to predict the dynamic responses of systems using the receptance coupling and frequency-based substructuring (RCFBS) method. The proposed approach is particularly suited for reconfigurable dynamic systems across various applications, like cars, robots, mechanical machineries, and aerospace structures. The methodology focuses on determining the overall system receptance matrix by coupling the receptance matrices (FRFs) of individual subsystems in a disassembled configuration. Two case studies, one with distributed parameters and the other with lumped parameters, are used to illustrate the application of this approach. The first case involves coupling three substructures with flexible components under fixed–fixed boundary conditions, while the second case examines the coupling of subsystems characterized by multiple masses, springs, and dampers, with various internal and connection degrees of freedom. The accuracy of the proposed method is validated against a numerical finite element analysis (FEA), direct methods, and a modal analysis. The results demonstrate the reliability of RCFBS in predicting dynamic responses for reconfigurable systems, offering an efficient framework for reduced-order modeling by focusing on critical points of interest without the need to account for detailed modeling with numerous degrees of freedom. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Vibration)
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