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Advances in Nonlinear Vibration: Modeling, Data-Based Methods and Applications

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Mechanical Engineering".

Deadline for manuscript submissions: closed (20 September 2024) | Viewed by 5443

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Dr. Dario Anastasio

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Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Interests: mechanical vibrations; nonlinear dynamics; nonlinear structural dynamics; system identification
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Stefano Marchesiello

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Guest Editor

Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Interests: linear and nonlinear system identification; nonlinear structural dynamics; moving loads
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Special Issue Information

Dear Colleagues,

Nonlinearity is known to play an important role in various fields of applied sciences. Structural nonlinearities, large-amplitude vibrations, limit cycles, instability, and friction are just some examples of nonlinear dynamical phenomena. The research community’s interest in improving our awareness of nonlinear vibration phenomena has gained increased importance in recent years, in combination with the incipient industrial need for efficient and lightweight designs, and the necessity of monitoring and characterizing pre-existent structures.

This Special Issue invites contributions on recent advances in nonlinear vibrations, focusing on modeling, data-based methods, and novel applications. Target topics include, but are not limited to, analytical and numerical methods, experimental nonlinear dynamics, signal processing, system identification and model updating, nonlinear phenomena in structures and structural health monitoring, nonlinear damping, dynamic interactions, nonlinear vibration control, and emerging topics in nonlinear vibrations.

Dr. Dario Anastasio
Prof. Dr. Stefano Marchesiello
Guest Editors

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Keywords

nonlinear dynamics
experimental nonlinear dynamics
nonlinear vibration
nonlinear modeling
data-based method
signal processing
nonlinear system identification

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Published Papers (4 papers)

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Research

21 pages, 17562 KiB

Open AccessArticle

Gear Fault Detection Method Based on Convex Hull Clustering of Autoencoder’s Latent Space

by Michał Batsch and Bartłomiej Kiczek

Appl. Sci. 2024, 14(12), 5282; https://doi.org/10.3390/app14125282 - 18 Jun 2024

Viewed by 1047

Abstract

This paper presents a method of pitting failure detection in toothed gears based on the reconstruction of the gear case vibrational signal. The effectiveness of the proposed method was tested in an experiment on a power circulation test stand. The autoencoder deep neural network architecture, semi-supervised training, and validation, along with the latent data convex hull-based clustering, are presented. The proposed method offers high efficiency (0.99 F1-measure) in gear state prediction (100% in failure detection, 98.9% in normal state prediction) and provides more capabilities in terms of generalization in comparison with linear machine learning techniques such as principal component analysis and nonlinear like the generative adversarial network. Moreover, it is distinguished by high sensitivity while also being able to detect even slight surface damage (initial pitting). These findings will be of particular relevance to a range of scientists and practitioners working with gear drives who are willing to implement machine learning in signal processing and diagnosis. Full article

(This article belongs to the Special Issue Advances in Nonlinear Vibration: Modeling, Data-Based Methods and Applications)

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17 pages, 4768 KiB

Open AccessArticle

Modal Derivatives for Efficient Vibration Prediction of Geometrically Nonlinear Structures with Friction Contact

by Fahimeh Mashayekhi and Stefano Zucca

Appl. Sci. 2024, 14(9), 3936; https://doi.org/10.3390/app14093936 - 5 May 2024

Viewed by 1024

Abstract

This paper evaluates the performance of the Rubin reduction methods, enhanced with static modal derivatives, for vibration analysis of geometrically nonlinear structures with friction contact. Static modal derivatives are computed numerically based on Rubin reduction, which includes free interface normal modes and residual flexibility attachment modes, by introducing a finite displacement around these modes. Then, the most relevant static modal derivatives are selected using an improved strategy that incorporates weighting factors derived from both a nonlinear static analysis and a geometrically linear transient run. This enhanced Rubin method is also compared with the previously used enhanced Craig–Bampton method, which is based on fixed normal modes, constraint modes, and their static derivatives. The effectiveness of these methods is demonstrated through vibration analysis of a geometrically nonlinear beam in different contact configurations. Both methods proved their robustness, achieving accurate results with a relatively small number of modes in the reduced space, thus ensuring low online computation times. Furthermore, the analyses show the significant impact of using a geometrically nonlinear model on the accurate prediction of a contact state. Full article

(This article belongs to the Special Issue Advances in Nonlinear Vibration: Modeling, Data-Based Methods and Applications)

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21 pages, 1241 KiB

Open AccessArticle

Quantitative Analysis of the Complex Time Evolution of a Camphor Boat

by Tomasz Roliński, Hiroyuki Kitahata, Yuki Koyano and Jerzy Górecki

Appl. Sci. 2024, 14(3), 959; https://doi.org/10.3390/app14030959 - 23 Jan 2024

Viewed by 1340

Abstract

The motion of a camphor boat on the water’s surface is a long-studied example of the direct transformation of chemical energy into a mechanical one. Recent experimental papers have reported a complex character of boat motion depending on the location of the camphor source. If the source is close to the stern, the boat moves at a constant speed. When it is shifted towards the boat center, oscillations of speed are observed. When the source is close to the boat center, pulses of speed followed by oscillations appear. Here, we focus on numerical simulations of camphor boat motion. We discuss approximations that allow us to reduce the numerical complexity of the problem and formulate a model in which the equation for boat velocity is coupled with a one-dimensional reaction–diffusion equation for camphor surface concentration. We scanned the phase space of model parameters and found the values that give qualitative agreement with the experiments. The model predicts all types of boat motion (continuous, oscillating, and pulsating) observed in experiments. Moreover, the model with selected parameter values shows that for specific locations of the camphor source, a spike in speed is followed by transient oscillations, which are an inherent part of speed relaxation. Full article

(This article belongs to the Special Issue Advances in Nonlinear Vibration: Modeling, Data-Based Methods and Applications)

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13 pages, 1416 KiB

Open AccessArticle

Reliability by Using Weibull Distribution Based on Vibration Fatigue Damage

by Jesús M. Barraza-Contreras, Manuel R. Piña-Monarrez and Roberto C. Torres-Villaseñor

Appl. Sci. 2023, 13(18), 10291; https://doi.org/10.3390/app131810291 - 14 Sep 2023

Cited by 6 | Viewed by 1409

Abstract

In this paper, a Weibull probabilistic methodology is proposed with an approach to model vibration fatigue damage accumulation using two parameters: Weibull distribution and a nonlinear fatigue damage accumulation model. The damage is cumulated based on the application of a vibration stress profile [...] Read more.

β

and

η

parameters, and the corresponding component reliability R(t). The vibration fatigue damage is analyzed to accumulate the damage as a stress function for a fatigue life exponent derived with the assistance of the acceleration’s force response. The steps to determine the Weibull

β

and

η

parameters are estimated based only on the principal vibration stresses

σ_{1}

and

σ_{2}

that allow the reproduction of the vibration fatigue damage. The method’s efficiency is based on the probabilistic approach by using the vibration fatigue damage as the Y_i vector that covers the arithmetic mean as well as the

β

parameter. Finally, the procedure proposed is applied in a practical case where a mechanical component is used as a support for telecommunication connections and is submitted to vibration stress. The results show that using the damage accumulated as the Y_i vector to estimate the parameters allows for the analysis of dynamic and individual applications. Full article

(This article belongs to the Special Issue Advances in Nonlinear Vibration: Modeling, Data-Based Methods and Applications)

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