Random Vibration Research Articles

Pseudo-equivalent model for sandwich panels with egg-shaped honeycomb-grid core

The novel sandwich panel with egg-shaped honeycomb-grid core (SP-EHC), formed by chamfering the grid walls, can achieve a balance between lightweight and high-strength, as well as promote effective ventilation and drainage due to the semi-closed honeycomb design. To determine the panel’s equivalent stiffness properties, an asymptotic analysis of the energy functional stored within the periodic unit cell is conducted. On this base, a 2D pseudo-equivalent model (2D-PEM) in the form of the Reissner–Mindlin model was formulated. The pseudo-excitation method was employed to analyze the self-power spectral density function and root mean square response of the 2D-PEM under random vibration. The accuracy and effectiveness of the model were validated through comparisons of the three-point bending experimental results of the 3D-printed specimen, exhibiting relative errors of 2.95%. In addition, free and random vibration analyses were conducted on the hybrid SP-EHC to further validate the model. Furthermore, the influence of material and structural parameters on specific stiffness, natural frequencies and first velocity RMS was systematically investigated. The findings reveal that enhancing the grid wall’s chamfering ratio is beneficial in achieving the desired objectives of lightweight and high-strength. In addition, compared to sandwich panels with orthogonal and pyramid grid cores, this improvement positively impacts the vibration characteristics of the sandwich panel. These findings offer valuable insights for the future design and optimization of such sandwich panels.

Mathematical model for assessing the influence of vibrations for multicopter elements

The article discusses the problem of studying the probabilistic characteristics of vibrations of the propellermotor group of an unmanned aerial vehicle such as a multicopter. The results of the research are presented in the form of quantitative values of the vibration parameters of the propeller-motor group of the agrodrone at given values of the input parameters of the electric drive control system, taking into account the influence of external factors. It is shown that the values of the parameters characterizing the vibrations of the propeller-motor group of the agrodrone can be different depending on the operating modes of the engines and changes in external conditions.Based on the experimental studies carried out, sets of measured random vibration parameters were obtained, which made it possible, based on the application of mathematical statistics methods, to calculate the mathematical expectations and dispersions of the amplitudes and velocities of vibration processes. The obtained probabilistic characteristics make it possible to study emissions (crossing a given level) of processes, to evaluate the intensity and probabilistic characteristics of the process going beyond the given boundaries.A mathematical model of the vibration process is substantiated, which allows, on the basis of the obtained experimental data, to assess the influence of vibrations on the elements of equipment installed on a multicopter, to assess its performance and reliability, and to determine tolerances on equipment parameters. The computer modeling of the probabilistic characteristics of vibration processes clearly demonstrated the efficiency of the proposed research methodology.

Effect of Creep, Fatigue and Random Vibration on the Integrity of Solder Joints in BGA Package

This study employs Finite Element Analysis (FEA) to investigate the effects of creep, fatigue, and random vibration on the integrity of solder joints in BGA packages in electronic modules. Evaluating the response of lead-based Sn63Pb37 and lead-free SnAgCu alloy solders (SAC305, SAC387, SAC396, and SAC405) to induced loads - stress, strain, strain energy density, and displacement in the joints is obtained and studied better to understand the mechanism of the joints' degradation. SAC305 and SAC405 are modelled with linear stress-temperature relationships σ = 3.152T–68.167 and σ = 1.543T–34.983, respectively. The magnitude of the strain energy density in the joints is a key failure driver. SAC387 and SAC396 solder joints display lower values of strain energy density and thus have higher durability. Displacement analysis indicates that SAC305 and Sn63Pb37 are prone to deformation-induced failure. SAC387 exhibits the highest fatigue yield stress at 58 MPa, while SAC405 displays the lowest stress at 22 MPa. Analysis of the results of random vibration shows that Sn63Pb37 developed the highest stress at 34.62 MPa and is thus susceptible to stress-induced failure. The robust stress, strain, and strain energy responses of SAC405 and SAC396 provide key insights into improving the mechanical reliability of future electronic devices towards better sustainability.

Random Vibration Characteristics and Vibration Suppression of an Aero-engine Inlet Rake Fabricated by Laser Powder Bed Fusion

The inlet rake is generally installed in aero-engine during rig and flight test for flow field pressure and temperature measuring. There are usually complex flow channels and pipelines inside the rake to extract air flow to the sensor. The laser powder bed fusion(L-PBF) technique was applied in rake fabrication recently due to its progressive layer stacking molding procedure. However, the difference of thermoforming method between L-PBF and the traditional casting process leads to the mechanical property disparities of the material. In this work, the determinants of random vibration response of the inlet rake manufactured by L-PBF with GH4169 powder were studied individually. The stiffness and yield property of the material were investigated by the specimen tensile test, which indicates higher elasticity modulus and yield stress comparing to the ones by castling or forging process. The damping ratio of the inlet rake was obtained through stress attenuation characteristics experiment and analysis under stepwise excitation. The stress distribution and resonance margin of the inlet rake under the aero-engine random vibration spectrum were simulated by finite element modal and random vibration analysis. The results showed that the damping ratio of the L-PBF inlet rake is much smaller than engineering recommendations, and the resonance margin is insufficient. Thus, the stress level of the inlet rake was very high, especially in the blade root section, quite close to the yield limit of the material. To solve this problem, the vibration suppression methods of the inlet rake were studied from the perspective of structural design optimization and damping ratio increasing. Through the rational design of the resonance margin and addition of vibration damping structure, the vibration stress of inlet rake was significantly suppressed. As the result, the rake was installed in the inlet during the aero-engine rig test for flow field pressure and temperature measurement successfully.

An attention-based deep learning method for safety of uncertain vehicle-bridge system with random near fault earthquakes

In this paper, a novel approach, based on the principle of the deep learning method, is proposed to study the stochastic responses of vehicle-bridge system (VBS) subjected to near fault earthquakes (NFEs), which also considers the effects of uncertain parameters. To generate the training data as the input of the proposed deep learning model, the dynamic formulas of the VBS are deduced by Newmark-β method. The proposed analysis model comprises three modules: the CNN module for seismic data feature extraction, the Attention Mechanism module for enhancing the selection for information between time series to improve the accuracy and efficiency of the final prediction, and the Bidirectional Gated Recurrent Unit (BiGRU) for predicting VBS responses. The mapping connection between earthquake action and the system response is established. The BiGRU model is capable of conveying both the excitation's randomness and the system's uncertain parameters. An actual railway cable-stayed bridge subjected to the running railway vehicle and NFEs is utilized to verify the proposed model. The uncertain train weight, bridge damping ratio and the randomness of NFEs are incorporated into the dynamic responses analysis of VBS. As a result, the time-varying responses obtained by the proposed model show significant agreement with results from a validated dynamic VBS framework. The mean value and standard deviation (STD) of the responses obtained by the proposed method are also compared with those by the Monte Carlo method and probability density evolution method. Therefore, both the individual sample of the dynamic response and the statistical data from diverse stochastic responses are chosen to validate the model's accuracy and efficiency in the VBS analysis under NFEs. In addition, the effects of the stochastic characteristics on the system's random vibrations are also explored through the time-histories of statistical data and the probability density function of the absolute maximum of responses.

Analysis of Vibration in Hybrid Composite Leaf Spring

Vibration-related failures more frequently occur than material failures, analysis is crucial to the design of composite leaf springs. It must also have an outstanding fatigue life and be lightweight. To minimize vertical vibrations, hits, and bumps caused by irregular roads and to ensure a comfortable ride, springs are essential suspension components in automobiles. Hence, the material with the highest strength and lowest longitudinal elastic modulus is ideal for use in leaf springs. In the automotive business nowadays, composite materials primarily replace metal elements. Consequently, it is important to use a hybrid composite leaf spring that evenly distributes graphite, carbon, and glass fibers throughout the resin matrix and has a lower spring rate. Hybrid composite materials offer many advantages over conventional composite materials because they use glass and carbon fibers instead of them. These advantages include maximum strength, minimum longitudinal modulus of elasticity, reduced weight as well as vibration, better packaging, enhanced durability, cost savings, fatigue life, and strain energy capacity. The first use of modal analysis is to determine Eigen-vectors, or mode shapes, and Eigen-values, or natural frequencies. Moreover, random vibration analysis is used to distinguish between smooth and rough vibrations, and harmonic analysis is used to determine the response’s amplitude.

Removal of movement artifacts and assessment of mental stress analyzing electroencephalogram of non-driving passengers under whole-body vibration.

The discomfort caused by whole-body vibration (WBV) has long been assessed using subjective surveys or objective measurements of body acceleration. However, surveys have the disadvantage that some of participants often express their feelings in a capricious manner, and acceleration data cannot take into account individual preferences and experiences of their emotions. In this study, we investigated vibration-induced mental stress using the electroencephalogram (EEG) of 22 seated occupants excited by random vibrations. Between the acceleration and the EEG signal, which contains electrical noise due to the head shaking caused by random vibrations, we found that there was a strong correlation, which acts as an artifact in the EEG, and therefore we removed it using an adaptive filter. After removing the artifact, we analyzed the characteristics of the brainwaves using topographic maps and observed that the activities detected in the frontal electrodes showed significant differences between the static and vibration conditions. Further, frontal alpha asymmetry (FAA) and relative band power indices in the frontal electrodes were analyzed statistically to assess mental stress under WBV. As the vibration level increased, EEG analysis in the frontal electrodes showed a decrease in FAA and alpha power but an increase in gamma power. These results are in good agreement with the literature in the sense that FAA and alpha band power decreases with increasing stress, thus demonstrating that WBV causes mental stress and that the stress increases with the vibration level. EEG assessment of stress during WBV is expected to be used in the evaluation of ride comfort alongside existing self-report and acceleration methods.

Numerical and experimental investigation of an auxetic piezoelectric energy harvester with frequency self-tuning capability

To deal with the limited availability of long-lasting power sources for sensor nodes in industrial environments, a novel piezoelectric energy harvester with high efficiency and a wide working bandwidth was designed to harvest broadband and random vibrations from the ambient environment. The developed energy harvester adopts a doubly clamped piezoelectric beam with a peanut-shaped auxetic structure to improve the power output. It also incorporates a sliding proof mass for frequency self-tuning, enabling a wider working bandwidth. As the doubly clamped beam exhibits geometry nonlinearity under large vibration amplitudes, the power output of the energy harvester can be further enhanced in the frequency self-tuning process. Finite element simulations are conducted to evaluate the impact of the auxetic structure and the position of the proof mass on the performance of the energy harvester. Experiments are performed to examine the energy harvesting performance of the proposed energy harvester. Under an excitation acceleration of 0.3 g, the use of the sliding proof mass widens the working bandwidth of the auxetic energy harvester (AEH) by 9 Hz, with the maximum root mean square output power of AEH reaching 18.78 μW, which is much higher than that of the plain energy harvester (PEH) or the AEH with a fixed proof mass. The developed energy harvester can successfully power a wireless temperature and humidity sensor node based on the vibration produced by a centrifuge, which demonstrates the practical feasibility of the proposed energy harvester for industrial applications.

A hybrid frequency‐time domain life prediction method based on the critical plane theory

AbstractThis study proposes a multiaxial rainflow counting method to realize simultaneous counting of four‐channel data. The power spectral density (PSD) expressions of stresses and strains in different planes are derived according to multiaxial theories to address the fatigue problems under random vibration loading. This study takes the plane with maximum variance of shear strain PSD as the critical plane and proposes a hybrid frequency‐time domain life prediction method for calculating the life under random vibration loading in combination with the proposed new multiaxial rainflow counting method. Both the feasibilities of the proposed multiaxial rainflow counting method and hybrid frequency‐time domain life prediction method are verified by using the multiaxial fatigue experimental results of 6061‐T6 and 7075‐T6 aluminum alloys under random loading. Meanwhile, the calculation results and efficiencies of the proposed life prediction method are summarized, and the prediction effects of the different multiaxial fatigue models are evaluated, and different rainflow counting methods are compared.

Model reference sliding mode control for two-degree-of-freedom electro-hydraulic shaking table

The multi-axis electro-hydraulic shaking table (EHST) is capable of simulating complex vibration environments to assess product reliability under vibrational excitation. The random vibration control method plays a crucial role in simulating these environments. However, the unmolded disturbances and the nonlinearity of the system have a significant impact on the control accuracy of the EHST. Sliding mode control (SMC) can be used in single-input single-output electro-hydraulic servo systems (EHSS) to attenuate the influence of disturbance forces. The conventional SMC is not suitable for acceleration random vibration control of the multi-axis EHST because the coupling between the axes and the actuators and the null bias of the servo valve are not taken into account. A model reference sliding mode control (MRSMC) is presented in this paper based on the nonlinear dynamic model of the EHST. The MRSMC designed based on the backstepping method and Lyapunov theory is used to compensate for the disturbance forces and the null bias of the servo valve. Experimental acceleration random vibration responses show that the MRSMC enhances the accuracy of tracking the acceleration random signal.

Study of the Extremely Low-Frequency Noise Characteristics of a Micro-Thrust Measurement Platform.

The critical structural parameters are optimized and studied using the numerical simulation method to improve the resolution and stability of the Micro-Thrust Measurement Platform (MTMP). Under two different ground random vibration environments, the parameters, such as pivot thickness, pendulum rod length, and pivot structure, are focused on analyzing the influence of the system's resolution and stability. The results show that when the thickness of the pivot is 0.04 mm or 0.2 mm, and the pendulum rod length is 2 m, the effect of ground random vibration on the MTMP is minimized. At 0.1 mHz, it can reach 0.0057 μN/Hz. In the series double-pivot structure, an appropriate increase in the distance between the sheets can further optimize the above conclusions. The results and analysis within this study can provide support for the engineering design of the MTMP.

Leakage mechanism model of proton exchange membrane fuel cell sealing structures under vibration conditions

ABSTRACT To resolve the issue of predicting the leak rate in proton exchange membrane fuel cells (PEMFCs) under long-term random vibration conditions. Considering the mechanism of bolt vibration loosening and rubber vibration relaxation, a leakage mechanism model of the PEMFC sealing structure under vibration conditions is proposed, and the validity of the model is verified by experimental comparison. The model clearly reveals the quantitative effects of structural parameters and material parameters on the leakage rate of PEMFC under vibration conditions. The research results show that under long-term random vibration conditions, the change of PEMFC leakage rate with time is mainly divided into three stages: response stage, stable stage, and leakage stage. Compared to bolt vibration loosening, the rubber vibration relaxation has a more significant impact on PEMFC leakage, the leakage rate of the fuel cell stack is 433ppm after 10,000 hrs of vibration. In addition, increasing the bolt preload, changing the bolt distribution, reducing surface roughness, and reducing gasket thickness can effectively suppress PEMFC leakage under random vibration conditions, the minimum leakage rate of the fuel cell stack can be reduced to around 170ppm per 10,000 hours. The proposed mechanism model provides an effective method for predicting the leakage rate of PEMFC sealing structures.

Computational homogenization for dynamic characterization of a square cellular honeycomb vibration energy harvester

The prevailing literature on homogenization of cellular structures mainly focuses on computing their effective properties, but only a few studies demonstrate their subsequent use in practical applications. Moreover, the emphasis is largely on static analysis, and dynamic studies are limited to free vibration analysis with no specific applications. Therefore, this research aims to address these gaps by assessing the effectiveness of finite element based homogenization approach in characterizing cellular vibration energy harvester. In particular, the study considers a square cellular structure in cantilever mode and demonstrates the dynamic characterization using the homogenization approach. The results from free, forced, and random vibration analysis show close conformance between cellular and homogenized models with a maximum error of less than 10%. Further, the homogenized model was used to characterize the electro-mechanical response of the square cellular vibration energy harvester, and the predicted voltages for the cellular and homogenized models were 11 V and 13.8 V, respectively, validating the accuracy of homogenized model. Also, the computational time is reduced by 50–75% when using the homogenized model, thereby providing a computationally efficient alternative to experimental and full-scale time intensive finite element simulations.

Research and optimization of vibration damping control for computer case

In order to effectively reduce the vibration of the product in the process of transportation, the cushioning pad is applied in the packaging of the computer case, which can not only greatly reduce the cost of the cushioning packaging design, but also promote the sales of the product. The vibration response of the key components in the computer case was tested and analyzed under the conditions of force hammer experiment and random vibration experiment, and the direct transmission rate of the buffer liner system to the key components was obtained. The excitation of three vibration levels of the standard truck vibration spectrum was used to simulate the excitation of different intensities in actual transportation, and the excitation acceleration power spectrum was obtained. The direct transmission rate quantified the vibration transmission characteristics of each buffer pad to the key components, and the size of the direct transmission rate reflected the degree of vibration energy absorption of each buffer pad to the key components. The critical buffer pad was optimized to absorb more vibration energy by increasing the buffer area of the critical buffer pad, reducing its vibration transmission capacity in the main resonance area.

Experimental study on flow-induced vibrations of an equilateral triangular prism with a high mass ratio

The mass ratio exerts a significant influence on the vibration responses exhibited by a bluff body in cross flows. In this investigation, the flow-induced vibration (FIV) of a transversely oscillating equilateral triangular prism, characterized by a high mass ratio (m* = 23.15), is experimentally examined to enhance our comprehension of these influences at elevated m*. Various angles of attack (AoA), ranging from α = 0°–60° with 5° increment, where α = 0° and 60° correspond to scenarios of one vertex facing upstream and downstream, respectively. The reduced velocity ranged from Ur = 3.0 to 31.0. The vibration responses are categorized into four regimes according to amplitudes and spectral characteristics: no vibration (α = 0°–20°), intermittent galloping (α = 25°), separated vortex-induced vibration (VIV) and galloping (α = 30°–35°), and galloping (α = 40°–60°). The implications of high m* are profound in the intermittent galloping regime, characterized by random and intermittent vibration responses, which is uniquely observed in the FIV of a triangular prism with a high mass ratio. Additionally, for FIV at high m*, the onset of galloping occurs at a notably lower Ur, and the restart of the prism's vibration in separated VIV and galloping regime is initiated by lower harmonic synchronization. Hard galloping is discerned exclusively at α = 60°, and the distinctions from soft galloping are deliberated.

Multi-sensor data fusion reconstruction method for vibration dynamic responses of aerospace structures

The dynamic responses of key locations are important inputs for the life and reliability assessment of spacecraft structures. Due to the limited sensing resources, most critical responses are difficult to measure directly. A structural dynamic response reconstruction method is necessary. The responses of target locations can be reconstructed based on the empirical mode decomposition (EMD) of measured signals and the modal superposition. However, the structural modal information contained in the measured signal of a single sensor is limited, affecting the reconstruction accuracy. In this paper, a response reconstruction method based on multi-sensor data fusion is proposed. It is applied to a main load-bearing structure of a spacecraft and its typical components to verify its strain response reconstruction effect under random vibration loads. The experimental results show that multi-sensor data fusion improves the strain reconstruction accuracy. The maximum reduction in reconstruction error is from 8.7% to 1.3%. The reconstruction accuracy is further improved with the increase in the number of sensors. The optimal weighted fusion strategy for this problem is the weights defined by the Euclidean distance (EUC) or the dynamic time warping distance (DTW). The fusion results show a better performance with the increase in the power of the defined distance. The proposed multi-sensor fusion method improves the reconstruction accuracy via supplementing structural information to each other and eliminating the instability of single measured signals. More accurate dynamic responses via reconstruction reduce the large input uncertainty in life prediction and lay the foundation for building structural digital twins and managing structural health more effectively.

Stress isolations for resonant pressure micro sensors

This paper presents stress isolations for resonant pressure micro sensors that are supported by fixed isolation layers during assembly. While the resonant frequencies of the two resonators experience shifts due to measured pressures, they are susceptible to environmental perturbations. The proposed stress-isolated assembly in this study effectively mitigates the adverse effects of environmental noise and stabilizes the intrinsic frequencies of the resonators. Specifically, when subjected to temperature variations within the range of -55∼85 °C, the accuracy of the stress-isolated resonant pressure microsensor was determined to be ±0.01% FS. Similarly, during 3-axis random vibration tests, the accuracy of these stress-isolated resonant pressure microsensors was quantified as ±0.01% FS in response to environmental vibrations.

Response spectrum-based analysis of airborne radar random vibration and multi-point control improvement

During the flight of a UAV (unmanned aerial vehicle), the LiDAR device undergoes random vibrations due to the changing flight attitude and wind speed conditions of the UAV. It is important to control the frequency and amplitude of the vibrations within a reasonable range by means of a damping structure. As the vibrations caused by various factors during flight are random and non-linear, this paper innovates the analysis principle and damping control means for the random vibrations of airborne optoelectronic devices. The response spectrum analysis theory is used to establish the shock response spectrum, and an optimised and improved recursive digital filtering method is used to fit the frequencies of random vibration to the synthetic shock response. Considering the uncertainty of the vibration excitation signal, a virtual excitation method is used for the first time to simulate the random vibration to which the radar may be subjected in the air, and to simplify the calculation steps. The shock plate structure is designed using a multi-point control method to innovate a passive response to the random excitation. Finally, a modal analysis of the synthesised impact response was carried out. It is verified that the first six modal frequencies are controlled within 220 Hz, realising the frequency reduction. The amplitude of the three x, y, and z directions is controlled to within 0.5 mm, thus achieving vibration damping.

Effect of lead-free solder thermal interface material thickness on the reliability of electronic components in a random vibration environment

The reliability of electronic components has persistently posed challenges for engineers. This study addresses the critical need of understanding the impact of random vibration on the reliability of lead-free solder as thermal interface materials (TIM) within electronic components. ANSYS software was deployed to design, develop, and simulate the electronic model, with a focus on the TIM. SAC405 lead-free solder served as the TIM, its thickness was varied between 0.01 to 0.06 mm (at 0.01 mm intervals). The results from this investigation reveal relevant correlations. As the TIM thickness increases, there's a noticeable reduction in stress and strain while the deformation increases. Remarkably, a direct relationship emerges between TIM thickness and fatigue life; thicker TIM correlates with increased fatigue life. In addition, at a TIM thickness of 0.01 mm, the fatigue life measurements were 2.76 x 104, 1.63 x 104, and 0.792 x 104 for Equations 1, 2, and 3, respectively. These findings carry profound implications for engineers, serving as a guiding framework to aid in the selection of optimal TIM thickness for electronic components if lead-free solders are used as TIM. Understanding these trade-offs between stress, strain, deformation, and fatigue life is pivotal, empowering engineers to make informed decisions during electronic system design and development, ultimately enhancing overall reliability. Using lead-free solders as TIM in electronic applications is proposed by this study due to the thermal and reliability benefits presented.

Numerical Simulation and Influence of Non-Gaussian Vibrations on Flexible Robotic Systems

Random vibration excitation is a standard method for obtaining the dynamic properties of aerospace structures and simulating loading conditions. Shaker-based random excitation and traditional finite element analysis techniques use random vibrations, assuming a Gaussian distribution of excitation impulse magnitudes. While Gaussian signals may sufficiently describe some vibrational environments, many real-world excitations have non-Gaussian distributions. These signals may contain vibrational impulses larger than those observed in a Gaussian signal and could cause damage if not considered. This paper examines the influence of non-Gaussian signals on flexible vs. rigid robotic architectures using NASA JPL’s Pop-Up Flat Folding Explorer Robot (PUFFER) and Cooperative Autonomous Distributed Robotic Explorer (CADRE). The results indicate that flexible systems can be significantly impacted by a non-Gaussian excitation profile and that neither a typical enveloping of a Gaussian excitation nor a superposition of the responses to a worst-case impulse load with the response to a Gaussian signal was sufficient to bound the response due to non-Gaussian excitation. The driving mechanism for increased sensitivity of flexible robotic systems appears to be inertial, and designers may consider shifting the relative flexibility of the system or its constraints to force particular deformation modes or designing hinge mechanisms with increased damping to minimize the influence of non-Gaussian signals on the response of a flexible robotic structure.