Random Vibration Research Articles

A novel framework for fatigue hotspot localization and damage assessment of multi-defect marine structures under random vibration

In ocean engineering, assessing vibration-induced fatigue under random loads is critical, particularly for ocean structures with multiple defects, as fatigue is highly sensitive to local structural flaws. Recently, incorporating structural dynamic characteristics into vibration fatigue assessments has emerged as a significant trend and formidable challenge, involving three key obstacles: precise localization of fatigue hotspots, extraction of key modes, and determination and integration of modal damage contributions. This paper introduces a novel framework for fatigue hotspot localization and damage assessment in the context of random vibration fatigue in ocean structures. By initially identifying fatigue hotspots and hot regions using stress mode shapes, refining the finite element mesh in hot regions, and conducting reanalysis, the exact locations of fatigue hotspots can be determined, enabling structural dimensionality reduction. The introduction of a modal damage contribution factor allows for the evaluation of each mode's damage contribution and the identification of key modes, further facilitating modal reduction. For the precisely localized fatigue hotspots, the proposed method combines the damage contributions of key modes, enabling rapid and accurate assessment of fatigue damage under random vibration loads. Finite element case studies and vibration fatigue test results demonstrate that the proposed framework effectively addresses the challenges of random vibration fatigue evaluation, achieving structural and modal reduction while significantly enhancing the efficiency of damage assessment without compromising accuracy.

Multi-direction vibration isolation via transverse isotropy control of metal rubber

Abstract Metal rubber (MR) is widely used for vibration isolation due to its high damping and designable stiffness, but the isolation efficiency is relatively low in the non-molding direction due to its transverse isotropy. In this paper, the transverse isotropy of MR is controlled by design of manufacturing parameters (wire diameter, spiral diameter and compression ratio), material parameter (relative density) and geometric structure, to improve the isolation efficiency in the non-molding direction. Firstly, the helix unit was adopted to establish the relation between the transverse isotropy of MR material and manufacturing parameters, and manufacturing parameters were designed to control the transverse isotropy of MR material. Next, based on parametric modeling and genetic algorithm, material parameters and geometric structure were optimized to control the transverse isotropy of MR isolator. Finally, the transverse isotropy of the designed MR isolator was tested by quasi-static experiments, and multi-direction vibration isolation performance was verified by random vibration experiments. It is demonstrated that the transverse isotropy is controlled efficiently, and the vibration isolation efficiencies of the proposed MR isolator are all up to 85% under 15-2000Hz broadband random vibration in X, Y and Z directions.

A novel method for failure probability prediction of plain weave composites considering loading randomness and dispersion of strength

A new method based on combined residual stiffness-strength degradation is developed to predict the failure probability of plain weave composites subjected to random fatigue loadings. All the parameters presented in the proposed analytical model are characterized using the outcomes from quasi-static and constant amplitude fatigue testing. The evolution of residual strength is obtained based on combined residual stiffness-strength degradation model, which can greatly reduce the cost of the experiments. The Weibull distribution with two parameters is used to account for the dispersion of residual strength. Combing with randomness statistics of the fatigue loadings and the interference criterion of stress-strength, the fatigue failure behavior and failure probability are obtained. The narrow-band random vibration experiments were conducted to generate the random loadings and validate the predicted results. The approach proposed in this paper takes full advantage of residual stiffness or residual strength method and has better accuracy.

Probabilistic correlations for resource loading regimes during transportation

There are several cases during exploitation of structures when external loading is random vibration in nature. It is, firstly, automobile and railway transporting regimes. Therefore, during formation of loading regimes for estimation of resource strength of structures probability-statistical approach is used. In this article basic principles of this approach for formation spectrums of cyclic loading for testing and analysis of resource strength are presented. Estimation of levels of cyclic loading is performed, as well as suggestions for possible use of proposed approach when estimating resource strength of structures were provided.

Random Vibration Analysis of High-speed Moving Maglev Train on Simply Supported Bridge Considering Track Irregularity

Random Vibration Analysis of High-speed Moving Maglev Train on Simply Supported Bridge Considering Track Irregularity

Fatigue Life Based Study of Electronic Package Mounting Locations on Printed Circuit Boards Subjected to Random Vibration Loads

Fatigue Life Based Study of Electronic Package Mounting Locations on Printed Circuit Boards Subjected to Random Vibration Loads

Coupled critical plane-pseudo excitation method for multiaxial fatigue analysis of structures under random vibration

This study proposes a coupled critical plane–pseudo excitation method for assessing multiaxial fatigue damage in mechanical structures subjected to random loads. Within the modal coordinate framework, we derive an expression for the spectral moment of the structural stress response using the pseudo excitation method, which facilitates the decoupling of spatial characteristics from frequency domain properties. For the input power spectral density, represented as an integer power function, we employ eigenvalue decomposition and the residue theorem to derive an analytical expression for the spectral moment of the modal displacement response. By constructing equivalent stress modes based on the maximum shear stress and normal stress criteria, we obtain an expression for the equivalent stress variance. Intelligent optimization algorithms are utilized to determine the critical plane position and the corresponding equivalent stress spectral moments, followed by the application of the Dirlik method for fatigue assessment. A numerical example involving random vibration multiaxial fatigue analysis of an L-shaped thin-walled plate demonstrates the effectiveness of the proposed coupled critical plane–pseudo excitation method in comparison to the traditional critical plane method that relies on the stress covariance matrix for calculating equivalent variance. The results confirm the accuracy and efficiency of our approach, and we further explore the impact of different forms of the excitation power spectral density and the damping ratios on the computational outcomes.

Study on Wear Debris Distribution and Performance Degradation of Electrical Connector Under Step Random Vibration Stress

Study on Wear Debris Distribution and Performance Degradation of Electrical Connector Under Step Random Vibration Stress

Dynamic optimization design of thin plate structure based on surrogate model

Abstract To enhance dynamic optimization efficiency in traditional thin plate structures, surrogate models are integrated for structural dynamic size optimization, reducing dependence on high-precision finite element simulations. This paper focuses on optimizing the aluminum alloy sheet as the subject of research. The parameters of the specimen are optimized through sensitivity analysis, based on the comparison between the free mode Finite Element Analysis (FEA) and Experimental Modal Analysis (EMA) results. The modified specimen undergoes validation under a four-edge clamped boundary condition. Subsequently, random vibration analysis is conducted to determine the root mean square (RMS) value of the acceleration response. Employing surrogate model technology, four models are constructed using parametric modeling and experimental design methods. These models are then compared for their fitting effectiveness. The results indicate that the RBF model exhibits the highest accuracy in fitting each response, effectively replacing dynamic simulation. Finally, the RBF combined with the NSGA-II method, optimizes the specimen’s structural size, resulting in a 21.6% reduction in mass and an 18.60% decrease in acceleration response. These outcomes demonstrate satisfactory optimization results, ensuring accuracy while enhancing the dynamic characteristics of the specimen structure. This research offers valuable insights for related engineering applications.

Spectral element method for random vibration analysis of the vehicle-track coupling system

In this paper, we propose a new random vibration analysis model for the vertical vehicle-track coupling system, which combines the symplectic method and the spectral element method (SEM) to enhance calculation efficiency and accuracy. The model assumed that the vehicle is composed of a multi-rigid body with 10 DOFs, and its motion equation is derived using the traditional frequency analysis method. Tracks are considered periodic structures, and the part between sleeper support points is considered a substructure. The motion equation of the periodic track-substructure is established by spectral element method (SEM), and the propagation of vibration wave between the substructures is calculated by the symplectic method. The frequency responses of the vehicle-track coupling system are calculated by using the German low-interference irregularity spectrum and short-wave irregularity spectrum as excitation. Then, the rationality of this method is verified by comparing it with the results from the traditional symplectic method and simulations using Universal Mechanism software. The comparison shows that this method surpasses the traditional symplectic method in high-frequency accuracy while maintaining high computational efficiency. Although the finite element method also has the capability for high-frequency analysis, this method can calculate the high-frequency vibration of an infinitely long track using just one element, making it more suitable for the efficient analysis of vehicle-track coupling systems. Finally, the model is applied to analyze the distribution characteristics of the vibration response of the coupled system in the frequency domain.

PB-MNSGA-II algorithm and its application for multi-objective optimization design of under-vehicle equipment

Structural damage caused to under-vehicle equipment under adverse working conditions affects the safe operation of high-speed electric multiple units (EMUs). To address the low optimization efficiency and take into account vibration fatigue in traditional under-vehicle equipment design, herein, a multi-objective optimization design method (PB-MNSGA-II) that combines particle swarm optimization-back propagation (PSO-BP) neural network and modified non-dominated sorting Genetic Algorithm II (MNSGA-II) was proposed. It can help engineers choose better equipment component thickness and achieve efficient and accurate design. First, MNSGA-II, the core content of PB-MNSGA-II, was proposed, which improved four aspects of NSGA-II: Latin hypercube sampling population initialization, adaptive crossover and mutation probability, mutation interference of Levy flight strategy, and optimal elite strategy. Then, zero-ductility transition (ZDT) series functions were employed to test MNSGA-II, thereby verifying its convergence and computational efficiency. Subsequently, utilizing the frame structure of the traction transformer (TTR) as an illustrative example, the PB-MNSGA-II approach was employed to enable multi-objective optimization. During this optimization process, the focus was on random vibration fatigue damage, thus enhancing the rationality of the optimization outcomes. After structural optimization, the mass of the TTR decreased by 20.1 kg, and the maximum vibration fatigue damage value decreased from 1.09 to 0.808, verifying the effectiveness and feasibility of the proposed method. The findings of this study provide important insights for the multi-objective optimization design of under-vehicle equipment under complex operating conditions.

Design and vibration test of first mirror mount assembly for ITER divertor VUV spectrometer

The divertor vacuum ultraviolet (VUV) spectrometer is a diagnostic system in the ITER tokamak, monitoring impurity content and behavior in the divertor region. The first mirror of the spectrometer, made of silicon carbide (SiC), is exposed to harsh environmental conditions, including high temperatures and significant inertial loads from electromagnetic disruption events. To ensure its reliable performance, we have designed and tested a robust mirror holder assembly. This paper introduces a novel design of the first mirror holder assembly for the ITER divertor VUV spectrometer and presents the results from comprehensive vibration tests conducted on a full-scale mock-up. The design features a double-holder structure with spring plate assemblies to accommodate thermal expansion and resist vibrational loads. The mock-up underwent a series of resonance search, sine dwell, and random vibration tests, replicating the expected loads during vertical displacement events in ITER. The mirror holder assembly and the dummy mirror successfully withstood the vibration tests without damage, validating the design for the ITER environment. The results demonstrate the robustness and reliability of the mirror holder assembly, ensuring the accurate and reliable operation of the divertor VUV spectrometer in ITER.

Development of fiber Bragg grating vibration sensor for bidirectional monitoring of thin rod cantilever beam

Monitoring of vibration frequencies and forces in cables and suspension rods of bridges is crucial. In order to achieve high-precision and bidirectional low-frequency monitoring of cable force and suspension rod, in this work, a thin rod cantilever beam type FBG vibration sensor was developed for bidirectional monitoring based on theory, experiment, and finite element simulation. Firstly, elastic structure of the thin rod was analyzed, and the structural parameters of the sensor were optimized based on theoretical analysis and finite element simulation. Then, the frequency and sensitivity of the sensor were tested. The obtained test results showed that the resonant frequency of the sensor in the x/y direction was 48 Hz, sensitivity was 90.5/102.3 pm/g, and error in frequency was less than 2 %. Furthermore, the force in the cable measured by the sensor was verified through indoor tension tests. The test results showed that the maximum error in the force measured in the cable was 0.86 % relative to the actual tension in the cable, indicating high measuring accuracy of the developed sensor. Finally, the sensor was applied to monitor forces in actual engineering cables, where an error of 4.21 % was noticed, which further validated the accuracy and applicability of the sensor. The research results of the present would provide guidance for improving the ability of the bidirectional low-frequency FBG vibration sensors to measure low-frequency random vibrations.

Simplified site response analysis for regional seismic risk assessments

Seismic risk assessment on a regional scale requires an estimation of ground motion intensity and its spatial variation over large geographical areas. This task is particularly challenging in the presence of very soft soil deposits where significant amplification occurs at specific frequencies that are often referred to as local resonances. It is often not feasible to conduct a nonlinear site response analysis at thousands of sites of interest across a region such as an urban area due to the computational effort involved and the required detailed information on soil profiles at each site. Thus, in regional seismic risk analyses the hazard is typically represented by a field of response spectral ordinates estimated by ground motion models. This study proposes a simplified site response analysis procedure to improve the characterization of spectral ordinates to be used in regional seismic risk assessments. In the proposed procedure, reduced-order models are used to conduct site response analysis using very few parameters to transform response spectra at rock outcrop into response spectra at the surface of each of the sites. A particular emphasis is given to soft-soil sites characterized by low shear-wave velocities overlaid on rock or firm soils. A non-uniform continuous shear beam model with a parabolic variation of shear modulus along the depth and modal damping is used in combination with Random Vibration Theory. It is shown that the proposed approach provides better estimates than those of ground motion models or physics-based ground motion simulation models which often cannot capture the local resonances. Site-specific validation of the shear beam model and overall simplified site response analysis is performed at four soft-soil sites in San Francisco, California. Despite its simplicity, it is shown that the proposed procedure adequately captures the amplitudes and spectral shapes of the motions. It is also shown that in conjunction with ground motion models or physics-based models, the proposed simplified site response analysis procedure can be used to efficiently simulate the seismic hazard on a regional scale through an example of a regional seismic hazard analysis of 160 softer soil sites in Downtown San Francisco during the Loma Prieta earthquake.

Design of compact signal source with reduced phase noise for airborne pulse Doppler RF sensor

Abstract In this article, a low phase noise signal source to be used as local oscillator in pulse Doppler radio frequency (PDRF) sensor is proposed. Innovative design techniques for realization of the low phase noise frequency source using phase-locked loop (PLL) and dielectric resonator (DR) are presented. Qualitative investigations have been carried out on the effect of phase noise in PDRF sensor performance. An X-band vibration resistant PLL-based frequency source with phase noise better than −95 dBc at 1 kHz frequency offset has been designed here. It also presents the design of a 7.6 GHz low phase noise, vibration resistant DR oscillator. Systematic analysis of the key design aspects, their thermal-vibrational stability, and ease of integration with hybrid microwave integrated circuits have been disclosed. A prototype board is fabricated, assembled in a compact mechanical enclosure of dimension 55 × 55 × 15 mm3. Finally, developed module is experimentally validated under 7.6 g rms magnitude random vibration test in three axes and compared results with other state of-the-art similar works. The comparison clearly shows the merit of present research work over other similar existing works.

Robust Targeted Energy Transfer with Asymmetric Nonlinear Energy Sinks Under Random Excitations

This study introduces an Asymmetric Nonlinear Energy Sink (ANES) to enhance robust Targeted Energy Transfer (TET) in vibration control. Traditional cubic Nonlinear Energy Sinks (NES) often struggle with varying excitation levels in random vibrations. The ANES integrates a cubic NES, extra inertia, and asymmetric stiffness components like a tension-only rope, two linear springs, and a viscous damper. The rope adds asymmetric stiffness by only applying tension force. This setup effectively absorbs vibrational energy across different levels of excitation, facilitating energy transfer from low-damped to high-damped modes. Numerical simulations demonstrate the ANES’s superior performance compared to traditional NES, supported by modal energy redistribution, Nonlinear Normal Modes (NNM) analysis, and Frequency-Energy Plots (FEP). These findings suggest that this type of ANES is a promising advancement for practical NES applications in vibration control.

Nonlinear normal modes and response to random inputs of systems with bilinear stiffness

This work seeks to provide a comprehensive review of the effects that stiffness bilinearity can have on the nonlinear modes of a system, its response in a random vibration environment, and the connection between the two. Stiffness bilinearity here refers to a continuous piecewise linear force vs displacement function that is composed of two linear regions. This work focuses on a bilinear stiffness function that is regularized so there is a smooth transition at the point where the two linear regions meet. A single-degree-of-freedom system (SDOF) and a two-degree-of-freedom (2DOF) system are explored and several interesting behaviors are shown. The SDOF bilinear spring model is characterized by four parameters: the low amplitude frequency, the ratio of the linear stiffnesses on either side of the transition, the displacement at which the transition occurs, and the rate or sharpness of the transition. The effect of each parameter on the shape of the NNM is described. In a 2DOF system, these parameters have similar effects, but modal coupling is found to play a significant role. When a bilinear system is subjected to random excitation, many harmonics appear in the response for both the SDOF and 2DOF cases. The root-mean-square (RMS) response of the bilinear system can be larger or smaller than the corresponding linear case depending on the values of the parameters and the type of forcing (broadband, bandlimited, in the shape of a vibration mode, etc.). However, many cases were observed in which the RMS response of the bilinear system was almost the same as that of a linear system, and hence the response could be predicted well using linear analysis. It is hoped that the results presented herein can assist engineers in helping to determine when linear analysis would be adequate to predict the failure of a system, when a rigorous nonlinear analysis is required, and what phenomena are likely to be observed in the latter case.

Harmonic Components Isolation in Vehicle Vibrations: Enhancing Quarter-Car Model Analysis with an Extended Kalman Filter Approach

<div>This article addresses the essential task of understanding vibrations produced by vehicles to enhance the design of authentic laboratory tests. The article focuses on two primary sources of vibrations: those arising from vehicle–road surface interaction, which is largely random, and those emanating from the drivetrain, characterized as a summation of harmonics with a time-varying fundamental frequency. The method involves the application of the extended Kalman filter (EKF) paired with robust nonlinear least-squares (NLS) initialization to isolate the harmonic components effectively. Through a comprehensive analysis involving mean-square-error (MSE) evaluation via Monte Carlo simulation, considering additive white Gaussian noise (AWGN) and a two-degrees-of-freedom quarter-car model’s simulation response to the road, the research demonstrates the EKF’s proficiency. The results indicate the EKF’s capability to accommodate AWGN with a signal-to-noise ratio (SNR) up to 0 dB and road-induced random background vibrations up to an SNR of −3 dB, maintaining an MSE order of approximately 10<sup>−3</sup>.</div>

Thermal-biomechanical manikin applied in turbulent airflow and vibration systems in transient conditions

This paper applied a thermal-biomechanical manikin in turbulent airflow and vibration systems in transient conditions. This numerical model evaluated the thermal and biomechanical components to which the human body is subjected. The first one considers the first-order equations systems based on the thermal numerical model, while the second one considers the second-order equations systems based on the vibration numerical model. This second-order equations system is converted into a first-order equation system. The resolution of the thermal and biomechanical numerical models is made through the Runge-Kutta-Fehlberg method with error control. The thermal numerical model is used in the study of the steady-state and transient conditions when the skin is subjected to mean and turbulent airflow. The biomechanical numerical model is used in the study of the human body vibrations applied to the feet, that a standing person is subjected, using periodical and random vibration signals of the floor. The thermal analysis shows that with an air fluctuation velocity, the skin temperature reduces slightly. The amplitude of the vibration in the lower body section is higher than in the upper body section. The introduction of the randomised vibration, in the periodical vibration, the human body vibration increases the fluctuation level.

Random Vibration Testing with Specified Fatigue Damage Spectrum and Preserved Power Spectral Density

Random Vibration Testing with Specified Fatigue Damage Spectrum and Preserved Power Spectral Density