Vibration

15 pages, 1286 KiB

Open AccessArticle

Weibull Reliability Based on Random Vibration Performance for Fiber Optic Connectors

by Jesús M. Barraza-Contreras, Manuel R. Piña-Monárrez, María M. Hernández-Ramos and Secundino Ramos-Lozano

Vibration 2025, 8(3), 46; https://doi.org/10.3390/vibration8030046 - 12 Aug 2025

Abstract

Communication via optical fiber is increasingly being used in harsh applications where environmental vibration is present. This study involves a Weibull reliability analysis focused on the performance of fiber optic connectors when they are subjected to mechanical random vibration stress to simulate real-world [...] Read more.

Communication via optical fiber is increasingly being used in harsh applications where environmental vibration is present. This study involves a Weibull reliability analysis focused on the performance of fiber optic connectors when they are subjected to mechanical random vibration stress to simulate real-world operating conditions, and the insertion loss (IL) degradation is measurable. By analyzing the testing times and stress levels, the Weibull shape (

β

) and scale (

η

) parameters are estimated directly from the maximal and minimal principal IL stresses (

σ_{1}

,

σ_{2}

), enabling the prediction of the connector’s reliability with efficiency. The sample size n is derived from the desired reliability (R(t)), and the GR-326 mechanical vibration test (2.306 Grms for six hours) is performed on optical SC angled physical contact (PC) polish fiber endface connectors that are monitored during testing to evaluate the IL transient change in the optical transmission. The method is verified by an experiment performed with

σ_{1} = 0.3960

and

σ_{2} = 0.1910

where the IL measurements are captured with an Agilent N7745A source-detector optical equipment, and the Weibull statistical results provide a connector’s reliability R(t) = 0.8474, with a characteristic value of

η

= 0.2750 dB and

β

= 3. Finally, the connector’s reliability is as worthy of attention as the telecommunication sign conditions. Full article

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33 pages, 1196 KiB

Open AccessArticle

Theoretical Formulations of Integral-Type Frequency–Amplitude Relationships for Second-Order Nonlinear Oscillators

by Chein-Shan Liu, Chia-Cheng Tsai and Chih-Wen Chang

Vibration 2025, 8(3), 45; https://doi.org/10.3390/vibration8030045 - 11 Aug 2025

Viewed by 238

Abstract

The development of simple and yet accurate formulations of frequency–amplitude relationships for non-conservative nonlinear oscillators is an important issue. The present paper is concerned with integral-type frequency–amplitude formulas in the dimensionless time domain and time domain to accurately determine vibrational frequencies of nonlinear [...] Read more.

The development of simple and yet accurate formulations of frequency–amplitude relationships for non-conservative nonlinear oscillators is an important issue. The present paper is concerned with integral-type frequency–amplitude formulas in the dimensionless time domain and time domain to accurately determine vibrational frequencies of nonlinear oscillators. The novel formulation is a balance of kinetic energy and the work during motion of the nonlinear oscillator within one period; its generalized formulation permits a weight function to appear in the integral formula. The exact values of frequencies can be obtained when exact solutions are inserted into the formulas. In general, the exact solution is not available; hence, low-order periodic functions as trial solutions are inserted into the formulas to obtain approximate values of true frequencies. For conservative nonlinear oscillators, a powerful technique is developed in terms of a weighted integral formula in the spatial domain, which is directly derived from the governing ordinary differential equation (ODE) multiplied by a weight function, and integrating the resulting equation after inserting a general trial ODE to acquire accurate frequency. The free parameter is involved in the frequency–amplitude formula, whose optimal value is achieved by minimizing the absolute error to fulfill the periodicity conditions. Several examples involving two typical non-conservative nonlinear oscillators are explored to display the effectiveness and accuracy of the proposed integral-type formulations. Full article

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27 pages, 4883 KiB

Open AccessArticle

Stochastic Vibration of Damaged Cable System Under Random Loads

by Yihao Wang, Wei Li and Drazan Kozak

Vibration 2025, 8(3), 44; https://doi.org/10.3390/vibration8030044 - 4 Aug 2025

Viewed by 287

Abstract

This study proposes an integrated framework that combines nonlinear stochastic vibration analysis with reliability assessment to address the safety issues of cable systems under damage conditions. First of all, a mathematical model of the damaged cable is established by introducing damage parameters, and [...] Read more.

This study proposes an integrated framework that combines nonlinear stochastic vibration analysis with reliability assessment to address the safety issues of cable systems under damage conditions. First of all, a mathematical model of the damaged cable is established by introducing damage parameters, and its static configuration is determined. Using the Pearl River Huangpu Bridge as a case study, the accuracy of the analytical solution for the cable’s sag displacement is validated through the finite difference method (FDM). Furthermore, a quantitative relationship between the damage parameters and structural response under stochastic excitation is developed, and the nonlinear stochastic dynamic equations governing the in-plane and out-of-plane motions of the damaged cable are derived. Subsequently, a Gaussian Radial Basis Function Neural Network (GRBFNN) method is employed to solve for the steady-state probability density function of the system response, enabling a detailed analysis of how various damage parameters affect structural behavior. Finally, the First-Order and Second-Order Reliability Method (FORM/SORM) are used to compute the reliability index and failure probability, which are further validated using Monte Carlo simulation (MCS). Results show that the severity parameter η shows the highest sensitivity in influencing the failure probability among the damage parameters. For the system of the Pearl River Huangpu bridge, an increase in the damage extent δ from 0.1 to 0.4 can reduce the reliability-based service life of by approximately 40% under fixed values of the damage severity and location, and failure risk is highest when the damage is located at the midspan of the cable. This study provides a theoretical framework from the point of stochastic vibration for evaluating the response and associated reliability of mechanical systems; the results can be applied in practice with guidance for the engineering design and avoid potential damages of suspended cables. Full article

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8 pages, 968 KiB

Open AccessArticle

Method of Measuring the Dynamic Young’s Modulus Using a Reflective Fiber Optic Sensor of Vibration

by Tomasz Więcek and Zygmunt L. Warsza

Vibration 2025, 8(3), 43; https://doi.org/10.3390/vibration8030043 - 24 Jul 2025

Viewed by 201

Abstract

The paper describes the vibration method of measuring the dynamic Young’s modulus for a ferromagnetic steel element. The parameters of vibrations at the resonant frequency induced by an external magnetic field are studied for an unmagnetized and magnetized steel element. A fiber optic [...] Read more.

The paper describes the vibration method of measuring the dynamic Young’s modulus for a ferromagnetic steel element. The parameters of vibrations at the resonant frequency induced by an external magnetic field are studied for an unmagnetized and magnetized steel element. A fiber optic reflective sensor is used to study the vibration parameters of this element. The dynamic Young’s modulus is determined from these studies. A theory describing the amplitude of vibrations of the tested sample induced by the interaction of a magnetic field is developed and used. The conclusions resulting from the studies using this method on the experimental stand are discussed and the scope of its further studies are proposed. Full article

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17 pages, 8151 KiB

Open AccessArticle

FEA-Based Vibration Modal Analysis and CFD Assessment of Flow Patterns in a Concentric Double-Flange Butterfly Valve Across Multiple Opening Angles

by Desejo Filipeson Sozinando, Bernard Xavier Tchomeni and Alfayo Anyika Alugongo

Vibration 2025, 8(3), 42; https://doi.org/10.3390/vibration8030042 - 23 Jul 2025

Viewed by 622

Abstract

A concentric double-flange butterfly valve (DN-500, PN-10) was analyzed to examine its dynamic behavior and internal fluid flow across multiple opening angles. Finite Element Analysis (FEA) was employed to determine natural frequencies, mode shapes, and effective mass participation factors (EMPFs) for valve positions [...] Read more.

A concentric double-flange butterfly valve (DN-500, PN-10) was analyzed to examine its dynamic behavior and internal fluid flow across multiple opening angles. Finite Element Analysis (FEA) was employed to determine natural frequencies, mode shapes, and effective mass participation factors (EMPFs) for valve positions at 30°, 60°, and 90°. The valve geometry was discretized using a curvature-based mesh with linear elastic isotropic properties for 1023 carbon steel. Lower-order vibration modes produced global deformations primarily along the valve disk, while higher-order modes showed localized displacement near the shaft–bearing interface, indicating coupled torsional and translational dynamics. The highest EMPF in the X-direction occurred at 1153.1 Hz with 0.2631 kg, while the Y-direction showed moderate contributions peaking at 0.1239 kg at 392.06 Hz. The Z-direction demonstrated lower influence, with a maximum EMPF of 0.1218 kg. Modes 3 and 4 were critical for potential resonance zones due to significant mass contributions and directional sensitivity. Computational Fluid Dynamics (CFD) simulation analyzed flow behavior, pressure drops, and turbulence under varying valve openings. At a lower opening angle, significant flow separation, recirculation zones, and high turbulence were observed. At 90°, the flow became more streamlined, resulting in a reduction in pressure losses and stabilizing velocity profiles. Full article

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26 pages, 5716 KiB

Open AccessArticle

Study on Vibration Control Systems for Spherical Water Tanks Under Earthquake Loads

by Jingshun Zuo, Jingchao Guan, Wei Zhao, Keisuke Minagawa and Xilu Zhao

Vibration 2025, 8(3), 41; https://doi.org/10.3390/vibration8030041 - 11 Jul 2025

Viewed by 373

Abstract

Ensuring the safety of large spherical water storage tanks in seismic environments is critical. Therefore, this study proposed a vibration control device applicable to general spherical water tanks. By utilizing the upper interior space of a spherical tank, a novel tuned mass damper [...] Read more.

Ensuring the safety of large spherical water storage tanks in seismic environments is critical. Therefore, this study proposed a vibration control device applicable to general spherical water tanks. By utilizing the upper interior space of a spherical tank, a novel tuned mass damper (TMD) system composed of a mass block and four elastic springs was proposed. To enable practical implementation, the vibration control mechanism and tuning principle of the proposed TMD were examined. Subsequently, an experimental setup, including the spherical water tank and the TMD, was developed. Subsequently, shaking experiments were conducted using two types of spherical tanks with different leg stiffness values under various seismic waves and excitation directions. Shaking tests using actual El Centro NS and Taft NW earthquake waves demonstrated vibration reduction effects of 34.87% and 43.38%, respectively. Additional shaking experiments were conducted under challenging conditions, where the natural frequency of the spherical tank was adjusted to align closely with the dominant frequency of the earthquake waves, yielding vibration reduction effects of 18.74% and 22.42%, respectively. To investigate the influence of the excitation direction on the vibration control performance, shaking tests were conducted at 15-degree intervals. These experiments confirmed that an average vibration reduction of more than 15% was achieved, thereby verifying the validity and practicality of the proposed TMD vibration control system for spherical water tanks. Full article

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15 pages, 3336 KiB

Open AccessArticle

Design, Optimization, and Experimental Validation of Dynamic Vibration Absorber for Vibration Suppression in Cantilevered Plate Structures

by Linn Ye, Yiqing Yang, Wenshuo Ma and Wenjing Wu

Vibration 2025, 8(3), 40; https://doi.org/10.3390/vibration8030040 - 8 Jul 2025

Viewed by 554

Abstract

Vibration control constitutes a critical consideration in structural design, as excessive oscillations may precipitate fatigue damage, operational instability, and catastrophic failures. Dynamic vibration absorbers (DVAs), serving as passive control devices, demonstrate remarkable efficacy in mitigating structural vibrations across engineering applications. This study systematically [...] Read more.

Vibration control constitutes a critical consideration in structural design, as excessive oscillations may precipitate fatigue damage, operational instability, and catastrophic failures. Dynamic vibration absorbers (DVAs), serving as passive control devices, demonstrate remarkable efficacy in mitigating structural vibrations across engineering applications. This study systematically investigates the design of DVAs for vibration suppression of a cantilevered plate through integrated theoretical modeling, parameter optimization, structural implementation, and experimental validation. Key methodologies encompass receptance coupling substructure analysis (RCSA) for system dynamics characterization and H∞ optimization for absorber parameter identification. Experimental results reveal 74.2–85.7% vibration amplitude reduction in target mode, validating the proposed design framework. Challenges pertaining to boundary condition uncertainties and manufacturing tolerances are critically discussed, providing insights for practical implementations. Full article

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24 pages, 3945 KiB

Open AccessArticle

A Parameter Sensitivity Analysis of Two-Body Wave Energy Converters Using the Monte Carlo Parametric Simulations Through Efficient Hydrodynamic Analytical Model

by Elie Al Shami and Xu Wang

Vibration 2025, 8(3), 39; https://doi.org/10.3390/vibration8030039 - 7 Jul 2025

Viewed by 311

Abstract

This paper introduces a novel approach by employing a Monte Carlo simulation to investigate the impact of various design parameters on the performance of two-body wave energy converters. The study uses a simplified analytical model that eliminates the need for complex simulations such [...] Read more.

This paper introduces a novel approach by employing a Monte Carlo simulation to investigate the impact of various design parameters on the performance of two-body wave energy converters. The study uses a simplified analytical model that eliminates the need for complex simulations such as boundary elements or computational fluid dynamics methods. Instead, this model offers an efficient means of predicting and calculating converter performance output. Rigorous validation has been conducted through ANSYS AQWA simulations, affirming the accuracy of the proposed analytical model. The parametric investigation reveals new insights into design optimization. These findings serve as a valuable guide for optimizing the design of two-body point absorbers based on specific performance requirements and prevailing sea state conditions. The results show that in the early design stages, device dimensions and hydrodynamics affect performance more than the PTO’s stiffness and damping. Furthermore, for lower frequencies, adjustments to the buoy’s height emerge as a favorable strategy, whereas augmenting the buoy radius proves more advantageous for enhancing performance at higher frequencies. Full article

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22 pages, 7569 KiB

Open AccessArticle

Chaos Suppression in Spiral Bevel Gears Through Profile Modifications

by Milad Asadi, Farhad S. Samani, Antonio Zippo and Moslem Molaie

Vibration 2025, 8(3), 38; https://doi.org/10.3390/vibration8030038 - 6 Jul 2025

Viewed by 282

Abstract

Spiral bevel gears are used in a wide range of industries, such as automotive and aerospace, to transfer power between intersecting axes. However, a certain level of vibration is always present in the systems, primarily due to the complex dynamic forces generated during [...] Read more.

Spiral bevel gears are used in a wide range of industries, such as automotive and aerospace, to transfer power between intersecting axes. However, a certain level of vibration is always present in the systems, primarily due to the complex dynamic forces generated during the meshing of the gear teeth affected by the tooth profile. To address these challenges, this research developed a comprehensive dynamic model with eight degrees of freedom, capturing both translational and rotational movements of the system’s components. The study focused on evaluating the effects of two different tooth profile modifications, namely topology and flank modifications, on the vibration characteristics of the system. The system comprised a spiral bevel gear pair with mesh stiffness in forward rotation. The results highlighted that optimizing the tooth profile and minimizing tooth surface deviation significantly reduce vibration amplitudes and improve dynamic stability. These findings not only enhance the performance and lifespan of spiral bevel gears but also provide a robust foundation for the design and optimization of advanced gear systems in industrial applications, ensuring higher efficiency and reliability. In this paper, it was observed that some modifications led to a 68% reduction in vibration levels. Additionally, three modifications helped improve the vibrational behavior of the system, preventing chaotic behavior, which can lead to system failure, and transforming the system’s behavior into periodic motion. Full article

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21 pages, 1070 KiB

Open AccessArticle

Modeling Hysteretically Nonlinear Piezoelectric Composite Beams

by Abdulaziz H. Alazemi and Andrew J. Kurdila

Vibration 2025, 8(3), 37; https://doi.org/10.3390/vibration8030037 - 6 Jul 2025

Viewed by 283

Abstract

This paper presents a modeling framework for hysteretically nonlinear piezoelectric composite beams using functional differential equations (FDEs). While linear piezoelectric models are well established, they fail to capture the complex nonlinear behaviors that emerge at higher electric field strengths, particularly history-dependent hysteresis effects. [...] Read more.

This paper presents a modeling framework for hysteretically nonlinear piezoelectric composite beams using functional differential equations (FDEs). While linear piezoelectric models are well established, they fail to capture the complex nonlinear behaviors that emerge at higher electric field strengths, particularly history-dependent hysteresis effects. This paper develops a cascade model that integrates a high-dimensional linear piezoelectric composite beam representation with a nonlinear Krasnosel’skii–Pokrovskii (KP) hysteresis operator. The resulting system is formulated using a state-space model where the input voltage undergoes a history-dependent transformation. Through modal expansion and discretization of the Preisach plane, we derive a tractable numerical implementation that preserves essential nonlinear phenomena. Numerical investigations demonstrate how system parameters, including the input voltage amplitude, and hysteresis parameters significantly influence the dynamic response, particularly the shape and amplitude of limit cycles. The results reveal that while the model accurately captures memory-dependent nonlinearities, it depends on numerous real and distributed parameters, highlighting the need for efficient reduced-order modeling approaches. This work provides a foundation for understanding and predicting the complex behavior of piezoelectric systems with hysteresis, with potential applications in vibration control, energy harvesting, and precision actuation. Full article

(This article belongs to the Special Issue Nonlinear Vibration of Mechanical Systems)

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16 pages, 321 KiB

Open AccessArticle

The Association Between Vibrotactile and Thermotactile Perception Thresholds and Personal Risk Factors in Workers Exposed to Hand-Transmitted Vibration

by Fabiano Barbiero, Andrea Miani, Marcella Mauro, Flavia Marrone, Enrico Marchetti, Francesca Rui, Angelo Tirabasso, Carlotta Massotti, Marco Tarabini, Francesca Larese Filon and Federico Ronchese

Vibration 2025, 8(3), 36; https://doi.org/10.3390/vibration8030036 - 4 Jul 2025

Viewed by 440

Abstract

Background: Hand–arm vibration syndrome (HAVS) is a well-recognized occupational condition resulting from prolonged exposure to hand-transmitted vibration (HTV), characterized by vascular, neurological, and musculoskeletal impairments. While vibration exposure is a known risk factor for HAVS, less is understood about the role of personal [...] Read more.

Background: Hand–arm vibration syndrome (HAVS) is a well-recognized occupational condition resulting from prolonged exposure to hand-transmitted vibration (HTV), characterized by vascular, neurological, and musculoskeletal impairments. While vibration exposure is a known risk factor for HAVS, less is understood about the role of personal risk factors and, particularly regarding neurosensory dysfunction. This study aimed to examine the association between vibrotactile (VPT) and thermotactile perception thresholds (TPT) and individual risk factors and comorbidities in HTV-exposed workers. Methods: A total of 235 male HTV workers were evaluated between 1995 and 2005 at the University of Trieste’s Occupational Medicine Unit. Personal, occupational, and health-related data were collected, and sensory function was assessed in both hands. VPTs at 31.5 and 125 Hz and TPTs (for warm and cold) were measured on fingers innervated by the median and ulnar nerves. Results: Multivariable regression analysis revealed that impaired VPTs were significantly associated with age, higher daily vibration exposure (expressed as 8 h energy-equivalent A(8) values), BMI ≥ 25, smoking, vascular/metabolic disorders, and neurosensory symptoms. In contrast, TPTs showed weaker and less consistent associations, with some links to smoking and alcohol use. Conclusions: These findings suggest that, in addition to vibration exposure, individual factors such as aging, overweight, smoking, and underlying health conditions significantly contribute to neurosensory impairment and may exacerbate neurosensory dysfunction in a context of HAVS. The results underscore the importance of including personal health risk factors in both clinical assessment and preventive strategies for HAVS and may inform future research on its pathogenesis. Full article

49 pages, 9659 KiB

Open AccessArticle

Machine Learning Approach to Nonlinear Fluid-Induced Vibration of Pronged Nanotubes in a Thermal–Magnetic Environment

by Ahmed Yinusa, Ridwan Amokun, John Eke, Gbeminiyi Sobamowo, George Oguntala, Adegboyega Ehinmowo, Faruq Salami, Oluwatosin Osigwe, Adekunle Adelaja, Sunday Ojolo and Mohammed Usman

Vibration 2025, 8(3), 35; https://doi.org/10.3390/vibration8030035 - 27 Jun 2025

Viewed by 504

Abstract

Exploring the dynamics of nonlinear nanofluidic flow-induced vibrations, this work focuses on single-walled branched carbon nanotubes (SWCNTs) operating in a thermal–magnetic environment. Carbon nanotubes (CNTs), renowned for their exceptional strength, conductivity, and flexibility, are modeled using Euler–Bernoulli beam theory alongside Eringen’s nonlocal elasticity [...] Read more.

Exploring the dynamics of nonlinear nanofluidic flow-induced vibrations, this work focuses on single-walled branched carbon nanotubes (SWCNTs) operating in a thermal–magnetic environment. Carbon nanotubes (CNTs), renowned for their exceptional strength, conductivity, and flexibility, are modeled using Euler–Bernoulli beam theory alongside Eringen’s nonlocal elasticity to capture nanoscale effects for varying downstream angles. The intricate interactions between nanofluids and SWCNTs are analyzed using the Differential Transform Method (DTM) and validated through ANSYS simulations, where modal analysis reveals the vibrational characteristics of various geometries. To enhance predictive accuracy and system stability, machine learning algorithms, including XGBoost, CATBoost, Random Forest, and Artificial Neural Networks, are employed, offering a robust comparison for optimizing vibrational and thermo-magnetic performance. Key parameters such as nanotube geometry, magnetic flux density, and fluid flow dynamics are identified as critical to minimizing vibrational noise and improving structural stability. These insights advance applications in energy harvesting, biomedical devices like artificial muscles and nanosensors, and nanoscale fluid control systems. Overall, the study demonstrates the significant advantages of integrating machine learning with physics-based simulations for next-generation nanotechnology solutions. Full article

(This article belongs to the Special Issue Nonlinear Vibration of Mechanical Systems)

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22 pages, 6760 KiB

Open AccessArticle

Nonlinear Dynamics of a Coupled Electromechanical Transmission

by Antonio Zippo, Moslem Molaie and Francesco Pellicano

Vibration 2025, 8(3), 34; https://doi.org/10.3390/vibration8030034 - 20 Jun 2025

Cited by 1 | Viewed by 485

Abstract

The mechanical connection between a transmission system and an electric motor gives rise to a strong interaction between their respective dynamics. In particular, the coupling between an electric motor and a nonlinear spur gear transmission significantly influences the overall dynamic behavior of the [...] Read more.

The mechanical connection between a transmission system and an electric motor gives rise to a strong interaction between their respective dynamics. In particular, the coupling between an electric motor and a nonlinear spur gear transmission significantly influences the overall dynamic behavior of the integrated system. This study presents a detailed investigation into the electromechanical coupling effects between a permanent magnet synchronous machine (PMSM) and a nonlinear spur gear transmission. To focus on these effects, three configurations are analyzed: (i) a standalone gear pair model without motor interaction, (ii) a combined gear–motor system without dynamic coupling, and (iii) a fully coupled electromechanical system where the mechanical feedback influences motor control. The dynamic interaction between the motor’s torsional vibrations and the gear transmission is captured using the derivative of the transmission error as a feedback signal, enabling a closed-loop electromechanical model. Numerical simulations highlight the critical role of this coupling in shaping system dynamics, offering insights into the stability and performance of electric drive–gear transmission systems under different operating conditions. It also underscores the limitations of traditional modeling approaches that neglect feedback effects from the mechanical subsystem. The findings contribute to a more accurate and comprehensive understanding of coupled motor–gear dynamics, which is essential for the design and control of advanced electromechanical transmission systems in high-performance applications. Full article

(This article belongs to the Special Issue Nonlinear Vibration of Mechanical Systems)

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Vibration, Volume 8, Issue 3 (September 2025) – 13 articles

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