Random Vibration Research Articles

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.

The higher-order analysis of response for linear structure under non-Gaussian stochastic excitations with known statistical moments and power spectral density

The frequency-domain analysis method is a fundamental component of the random vibration analysis, in which the corresponding moment spectrum of excitations are the prerequisite. Nevertheless, the determination of the higher-order moment spectra for non-Gaussian stochastic excitations continues to pose a significant challenge in the existing research works. This paper introduces an accurate and efficient computational approach for determining higher-order moment spectra of non-Gaussian stochastic excitations with known statistical moments and power spectral density (PSD). Firstly, following the idea of the simulation method of non-Gaussian stochastic processes, the transformation model between the stationary non-Gaussian stochastic process and underlying Gaussian stochastic process is determined based on the known statistical moments, the PSD of the underlying Gaussian stochastic process is determined using the transformation model. Secondly, the approximate higher-order moment spectra models of stationary non-Gaussian stochastic processes are presented by the PSD of the underlying Gaussian process. Subsequently, the higher-order moment spectra models of non-Gaussian excitations are utilized to compute the higher-order moment spectra of response for the linear structure via the auxiliary harmonic excitation generalized method. Finally, three numerical examples are examined to assess the efficiency and accuracy of the proposed approximate models for the higher-order moment spectra of non-Gaussian stochastic processes.

Modal and random vibration responses of composite overwrapped pressure vessels with various geodesic dome trajectories

In the current study, Composite Overwrapped Pressure Vessels (COPVs) with various geodesic dome profiles have been built and their modal and random vibration responses were numerically examined. In this regard, geodesic dome profiles were established for five different polar opening radii of 10, 15, 20, 25, and 30 mm, and thus the impacts of fibre orientations on vibration characteristics depending on the filament winding trajectories were discovered. Furthermore, non-prestressed modal and random vibration responses for COPVs, as well as prestressed vibration behaviours under 50, 100, and 150 Bar internal pressure, were investigated and thus the effects of internal pressure severity on dynamic characteristics were identified. The study found that higher polar opening radius triggered a reduction in the natural frequencies, and these reductions were linked to an increment in the filament winding angle, and a consequent deterioration in the structural stiffness of COPVs. On the other hand, raising the internal pressure severity shifts the natural frequencies to higher frequencies, which are also attributed to ascended structural stiffness. Furthermore, it was established that internal pressure severity and polar opening radius had a coupled effects on the modal and random responses, and that both parameters should be evaluated simultaneously.

Dynamic modeling and reliability analysis of satellite antenna deployment mechanism based on parameter uncertainty

AbstractThis study delves into the factors that affect the reliability of satellite antenna deployment mechanisms. It employs the Kolmogorov–Smirnov (K‐S) test to quantify uncertainty characteristics, leading to the acquisition of pertinent stochastic parameters. Subsequently, three‐dimensional models and finite element models of the satellite antenna deployment mechanism are established using SOLIDWORKS and ANSYS software. Modal distribution, harmonic response analysis, random vibration analysis, and deployment process simulation are conducted. Parameterized modeling of the deployment mechanism's dynamics simulation process is performed, taking into consideration parameter uncertainty. Finally, a Kriging surrogate model is utilized to formulate an approximate expression between the factors influencing the reliability of the antenna deployment mechanism and its dynamic response. Based on the general stress‐strength interference theory, a reliability analysis model is constructed. Combined with active learning algorithms, this approach achieves efficient and precise calculations of the reliability of the satellite antenna deployment mechanism.

A framework proposal for new multiaxial fatigue damage and extreme response spectra in random vibrations frequency analysis

Fatigue Damage Spectra (FDS) and Extreme Response Spectra (ERS) are well-established tools for characterizing and evaluating the impact of vibration loads on mechanical structures. While this is particularly valuable in producing test-tailored specifications, their current application is limited to uniaxial analysis despite evidence indicating their inadequacy in representing real-world loads, which are often multiaxial.The proposed method offers a system-oriented approach to characterize and compare multiaxial environments in terms of their severity, independently or not of any physical structure. In addition, it introduces a generalization of the FDS and ERS, referred to as Fatigue Damage multi-Spectrum (FDmS) and Extreme Response multi-Spectrum (ERmS) respectively. These extensions allows for the consideration of multiaxial phenomena, such as correlation and modal proximity. Finally, this paper demonstrates through several case studies the method’s capability to capture phenomena not addressed by established uniaxial approaches.

Modified time domain randomization technique for multi-shaker non-stationary non-Gaussian random vibration control

Traditional random vibration environmental tests simulate stationary Gaussian random vibration environments. In this work, the generation and closed-loop control of multi-shaker non-stationary non-Gaussian random vibration signals with the modified time domain randomization technique are studied. The amplitude modulation function is introduced to control the non-stationary and non-Gaussian characteristics that the root mean square value of the generated signal changes with time. The kurtosis relationship between the one frame pseudo-random signal and consecutive true random signal is derived theoretically. It is found that the kurtosis of the consecutive non-stationary random signal is determined by the amplitude modulation function and kurtosis of the pseudo-random signal. The standard deviation of the time-varying root mean square reflects the non-stationary characteristics of the generated signal. A control strategy for multi-shaker non-stationary non-Gaussian random vibration environmental test is proposed. The non-stationary and non-Gaussian characteristics are extracted from the measured response signals so that the power spectral densities, kurtoses and non-stationary characteristics can be controlled simultaneously. The results from the simulation examples and multi-shaker vibration experiments prove the feasibility and practicability of the proposed non-stationary non-Gaussian random signal generation method and control strategy.

Random crowd-induced vibration in footbridge and adaptive control using semi-active TMD including crowd-structure interaction

A slender footbridge can suffer from a large vibration under vertical human-induced excitation. To improve its serviceability, a tuned mass damper (TMD) has a wide application. However, considering the randomness and synchronization of crowd-induced excitation and the effect of crowd-structure interaction (CSI), the control robustness of a passive TMD needs to be improved. To achieve a better performance, a semi-active TMD (STMD) with variable mass and damping (VMD-STMD) is presented in this paper, which can not only adjust the own mass and frequency in real time to adapt to the dynamic characteristics of the footbridge through the water pump and electromagnetic valve, but also adjust its damping to improve the effect of energy dissipation through changing the eddy current damping. The proposed VMD-STMD can maximize the absorption of structural kinetic energy and dissipate. The working mechanism and control algorithm of VMD-STMD are introduced first, and then, a Euler-Bernoulli simply supported beam is studied. To highlight the best control effect and robustness of VMD-STMD, an optimized passive TMD, variable mass STMD (VM-STMD) and variable damping STMD (VD-STMD) are compared, 100 calculations of them based on crowd probabilistic models are proposed. The influence of CSI is investigated and different crowd density and synergy rate are discussed in detail. Through the maximum, mean and standard deviation of the three comfort evaluation indexes of the 100 groups of acceleration, the control effect and robustness of different TMDs are analyzed. Results show that structural dynamic responses and TMD’s performance vary greatly due to the randomness of CSI. In general, VMD-STMD has the best control effect, and its standard deviation is also the smallest, indicating the best control robustness.

Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs

Random vibration analysis is a mathematical tool that offers great advantages in predicting the mechanical response of structural systems subjected to external dynamic loads whose nature is intrinsically stochastic, as in cases of sea waves, wind pressure, and vibrations due to road asperity. Using random vibration analysis is possible, when the input is properly modeled as a stochastic process, to derive pieces of information about the structural response with a high quality (if compared with other tools), especially in terms of reliability prevision. Moreover, the random vibration approach is quite complex in cases of non-linearity cases, as well as for non-stationary inputs, as in cases of seismic events. For non-stationary inputs, the assessment of second-order spectral moments requires resolving the Lyapunov matrix differential equation. In this research, a numerical procedure is proposed, providing an expression of response in the state-space that, to our best knowledge, has not yet been presented in the literature, by using a formal justification in accordance with earthquake input modeled as a modulated white noise with evolutive parameters. The computational efforts are reduced by considering the symmetry feature of the covariance matrix. The adopted approach is applied to analyze a multi-story building, aiming to determine the reliability related to the maximum inter-story displacement surpassing a specified acceptable threshold. The building is presumed to experience seismic input characterized by a non-stationary process in both amplitude and frequency, utilizing a general Kanai–Tajimi earthquake input stationary model. The adopted case study is modeled in the form of a multi-degree-of-freedom plane shear frame system.

Design of Stress Release Support Mechanism for Large-Size Body-Mounted Radiator

Design of Stress Release Support Mechanism for Large-Size Body-Mounted Radiator

Post-Fracture Stiffness and Residual Capacity Assessment of Film-Retrofitted Monolithic Glass Elements by Frequency Change

The primary goal of safety films for glass in buildings is to retrofit existing monolithic elements and prevent, in the post-fracture stage, any fall-out of shards. Their added value is that—as far as the fragments are kept bonded—a cracked film-glass element can ensure a minimum residual mechanical and load-bearing capacity, which is strictly related to the shards interlocking and debond. To prevent critical issues, such a mechanical characterization is both important and uncertain, and requires specific methodologies. In this regard, a dynamic investigation is carried out on fractured film-bonded glass samples, to assess their post-fracture stiffness trends and its sensitivity to repeated vibrations. The adopted laboratory layout is chosen to assess the effects of random vibrations (220 repetitions) on a total of 12 cracked specimens in a cantilever setup (with 0.5–5 m/s2 the range of randomly imposed acceleration peaks). By monitoring the cracked vibration frequency, the film efficiency and corresponding residual bending stiffness of cracked glass samples are quantified as a function of damage severity, with a focus on fragments interlock. Quantitative experimental estimates are comparatively analyzed and validated with the support of finite element (FE) numerical models and analytical calculations. As shown—at least at the small-scale level—a progressive post-fracture stiffness reduction takes place under repeated random vibrations, and this implicitly affects the residual load-bearing capacity of glass members. Most importantly, for the tested configurations, it is shown that the cracked vibration frequency is minimally affected by crack geometry, and follows a rather linear decrease with the number of imposed random impacts (up to an average of ≈20 for each sample), thus confirming the retrofit potential and efficiency in providing some mechanical capacity through fragments interlock.

Optimal multiple tuned mass dampers for monopile supported offshore wind turbines using Genetic Algorithm

This study investigates the parametric optimization of multiple-tuned mass dampers (MTMDs) deployed along the length of a tower and monopile structure subjected to stochastic wind and wave forces. The structural components, comprising the tower and monopile, are conceptualized as Euler–Bernoulli beams. The interaction with the soil is modeled through viscoelastic springs distributed along the monopile. The rotor nacelle assembly (RNA) and blades are abstracted into a concentrated mass at the tower’s apex. The MTMDs are characterized as spring–mass–dashpot systems strategically positioned at intervals along the tower and monopile. The investigation involves a random vibration analysis under wind and wave loads, employing the Kaimal spectrum for wind and the JONSWAP spectrum for waves. The study focuses on optimizing the TMD parameters using H2 optimization techniques, with the optimization criteria being the minimization of the standard deviation of the tower’s top displacement response. Additionally, meta-heuristic algorithms like the genetic algorithm (GA) are utilized to refine the determination of these optimal parameters. A key aspect of the research includes a parametric study that reveals variations in optimal parameters as the number of TMDs is altered, maintaining a consistent total mass across the MTMDs.

Magnetic-Control Variable Stiffness and Damping Tail Support for a Wind-Tunnel Aircraft Model

To suppress random vibration of aircraft models during wind tunnel tests, a novel magnetorheological elastomer (MRE)-based device with variable stiffness and variable damping (VSVD) is proposed, which is installed on the tail support system. Firstly, the dynamic characteristics of the tail support system are established using finite element model simulation to obtain the vibration mode and stress distribution. Next, the vibration reduction mechanism of the MRE-based tail support system is analyzed by solving a finite element model. Then, the magnetic-controlled VSVD device with an annular sandwich structure is proposed, and the decisive rheology material and structural parameters in relation to the tail support system’s dynamics are determined. Subsequently, the magnetically generated element with multicoils is designed to guarantee a large enough magnetic field, and the optimal structure parameters are obtained. Finally, random wind flow experiments in the wind tunnel and frequency sweep tests in the ground laboratory for the tail support system equipped on the VSVD device are conducted to verify the effectiveness of the proposed device, respectively. The results under 15–200 Hz random excitation indicate the root mean square of acceleration at the centroid of the aircraft model with the VSVD device can be decreased by 46.8% compared to the system without the VSVD device.

Developing a Robust Process for Design Margin Calculation Through Modal Scaling and Harmonic Analysis of Engine Mounted After Treatment System

The last few years have seen an increase in the complexity of emission standards. This has caused OEMs to start using Exhaust Gas Processors (EGP) or Exhaust After Treatment Systems (EATS)in complex integration. These systems are usually mounted on vehicle chassis or engine body with the help of mounting straps or brackets. The arrangement of the system leads to road loads and/or engine vibrations being transferred and causing damage to its components. New BS VI engines need some AT (After treatment) components to be mounted directly on the engine and others to chassis. The components that are directly mounted on engine are called close couple AT system which are subjected to engine harmonic vibrations which falls under forced vibration criteria. Most of the AT system are subjected to random vibrations and industry has a well-defined procedure to address the problem, but for harmonic vibrations there is no specific approach. In order to optimize the structural durability of close couple AT system against HCF (high cycle fatigue) fatigue harmonic vibration, there is a need for well-defined test analysis correlation procedure. The objective of this work is defining and documenting a robust process for design margin through calculation modal scaling and harmonic analysis of close couple AT system through test analysis correlation activity. Analytical, numerical and testing data were compared and conclusions are drawn. More case studies can be added to this work in order to validate the test analysis correlation activity and boost the degree of confidence. Future study may include recording additional failure modes in addition to the harmonic HCF failure mode.

Cable Cross‐Tie Triboelectric‐Electromagnetic Hybrid Generator Triggered by Vibrations in Bridge Cables

AbstractBridge cables exhibit low damping characteristics and are susceptible to external excitations, leading to random vibrations. Therefore, a cable cross‐tie triboelectric‐electromagnetic hybrid generator triggered by vibrations in bridge cables (CCT‐TEHG) is proposed. The CCT‐TEHG enhances the natural frequency of the cables by connecting adjacent cables, thereby preventing low‐frequency resonance. The device connects adjacent bridge cables to increase the natural frequency, preventing low‐frequency resonance. Comprising triboelectric nanogenerators (TENGs) and electromagnetic generators (EMG), the CCT‐TEHG effectively broadens the frequency range for energy harvesting, capturing vibrational energy from bridge cables in cable‐stayed bridges. The TENG module in CCT‐TEHG features a soft‐contact design, incorporating rabbit fur to supplement charges and enhance output density. This design also avoids direct material contact between generator units, improving operational durability. The experimental results show that the maximum output voltage and current of the TENG and EMG modules can respectively reach up to 270 V, 13 V, and 5.2 µA, 18 mA, and peak power to 2.04 mW, 10 mW. The CCT‐TEHG can function as a power source, sufficient to power 303 light‐emitting diodes (LEDs) or a 20 mW temperature and humidity sensor. Therefore, CCT‐TEHG has good application prospects in the field of bridge cable vibration energy harvest.