Random Vibration Loading Research Articles

Characterizing non-Gaussian vibration loading using the trispectrum

This paper addresses the use of higher-order spectra to study the non-Gaussian nature of random vibration loading. Since the power spectral density is only a full description for stationary Gaussian processes, specifying non-Gaussian random vibration loading requires a sophisticated statistical description. In recent research higher-order statistical moments such as skewness and kurtosis have been used to define non-Gaussian properties of vibration loading. However, useful information contained in the spectral representation of these moments is neglected. This paper introduces the trispectrum as a tool for analyzing vibration loading. It is the spectral representation of the fourth-order moment and thus extends the information content of the kurtosis. For demonstration several common methods for generating non-Gaussian loading are reviewed and used to derive loads that reproduce the power spectral density and kurtosis of a real in-service loading. These loads are analyzed using Fatigue Damage Spectra and trispectra to relate structural response behavior to their non-Gaussian nature. The results suggest that the trispectrum is a valuable tool for analyzing and classifying non-Gaussian random loading.

Static and Random Vibration Analyses of a University CubeSat Project

This work presents hands on experience of the configuration process and strength analyses of a student’s CubeSat project at the German University in Cairo. The static and dynamic performance of the primary structure, during launching phase, are investigated and checked against the strength requirements in addition to making sure that stiffness constraints imposed by the P-POD and the candidate launchers are met. The static response of the primary structure is performed using ANSYS Finite Element Software by exposing the structure to the maximum quasi static launch load in each of three flight directions separately. Modal analysis results are presented in order to check the compliance of the longitudinal and lateral natural frequencies, of the proposed model, with the launchers requirements. In addition, random vibration response is performed using frequency domain analysis, assuming that the structure will be subjected to launch random vibration loads in all directions. Finally, fatigue life analysis is presented in order to ensure that primary structure will safely survive the launching mechanical environments.

Failure analysis on the axial-connected bolts of the thin-walled cylinder under random vibration loading

The axial-connected bolts of the thin-walled cylinder structure product failed under random vibration loading acted in the transverse direction. The failure modes include pull-off of the thread on the nut as well as fracture of the bolt. The fracture appearance in fractographic study shows that the failure mechanisms of the bolt connections are shear strength failure of the thread on the nut and fatigue fracture of the bolt respectively. The FEM random vibration analysis was conducted on the overall structure, and the Power Spectral Density(PSD) of the axial force on the bolt was considered as the input loading of the shear strength failure life analysis on the nut as well as the fatigue life analysis on the bolt. Finally the fatigue experiment was conducted on the simplified bolt-connected structure for verification, which showed that the failure conditions and fatigue lives of the specimens were basically the same as those of the original product. Both the results of the fracture appearance analysis and the theoretical analysis are in accordance with those of the fatigue verification experiment, which confirms the failure mechanism of the product.

Comparison of fatigue life prediction methods for solder joints under random vibration loading

The fatigue life prediction of solder joints under random vibration load is one of the most important aspect in design of packaging. A fatigue-life estimation in the frequency domain is proved to have advantages in comparison to the time-domain estimation. This paper presents a comparison of the fatigue life prediction of solder joints under random vibration load by several popular frequency domain methods, including the narrow-band, the Wirsching–Light, the single-moment, the Empirical α0.75, the Tovo–Benasciutti, the Zhao–Baker, and the Dirlik methods. The comparison between these selected frequency domain methods and the traditional Steinberg method was investigated with the help of the relative error. Results indicate that most spectral methods are accurate than the Steinberg method, the Tovo–Benasciutti method is proved to be the best method for the life estimation of solder joints suited not only to the BGA package but also to the PoP package.

Random fatigue damage accumulation analysis of composite thin-wall structures based on residual stiffness method

The damage accumulation and life prediction for C/SiC composite panels subjected to random vibration loading was studied by using the residual stiffness model in combination with critical failure stiffness ratios in the different stress levels. According to the results of stiffness degradation and material S-N curves for constant-amplitude fatigue loadings, a new residual stiffness model was established and extended to adapt random stress states by using an equivalent damage ratio algorithm in time domain. The stiffness degradation and material S-N curves were obtained by using constant amplitude fatigue experiments. Random vibration tests with limited-bandwidth excitation were conducted to verify the prediction model. Good agreement is observed compared with the results of 2D plain-woven C/SiC composite panel subjected to random vibration loadings.

Fatigue assessment of amplitude-modulated non-stationary random vibration loading

Designing mechanical structures exposed to random vibration loading compromises the central challenges of defining comprehensive load assumptions and of processing these efficiently in a fatigue assessment. For this matter of statistical load description, frequency-domain methods withhold major advantages. They describe random vibration loading by its power spectral density, which allows drastic data reduction, to conduct efficient response analyses and to derive a statistical description of resulting load spectra. Nevertheless, this procedure is limited to stationary Gaussian loading. Thus, this paper proposes an extension of the frequency-domain approach to a special class of non-stationary loading – amplitude-modulated processes. These consist of a unique vibration state that varies in intensity, which is represented by a modulating signal. This paper develops a methodology to test for amplitude-modulated processes, to derive efficient measures for the intensity variation and to include this behavior in a fatigue assessment carried out in frequency-domain. The full methodology is presented via a set of simulated data.

Adapted Locati method used for accelerated fatigue test under random vibrations

Fatigue experiments are very important for the study of structural fatigue damage. As we all know, fatigue experiments usually consume a lot of resources and time, slowing down the research progress. The Locati method, which is applied to the frequency domain analysis method of random vibration fatigue, replaces the traditional up-down method and accelerates the progress of the fatigue experiment. This method can effectively improve efficiency and reduce test time and test piece consumption under the premise of ensuring accuracy. It is based on the material S-N curve, after one step-load fatigue test, combined with the FEM, the cumulative damage of the structure under random vibration load is quickly determined, and the life analysis is completed. The specimen was made by AISI304 and designed to make the fatigue damage of the second-order bending mode more significant. The random vibration acceleration defined by the Power Spectral Density method is used as a load and applied on the specimens through the shaker. In this process, the material properties of the structure will be optimally fitted according to the experimental results, so that the finite element model is as close as possible to the real structure for fatigue calculation. Finally, an experiment will be used to verify the accuracy of this method. The method has now been validated under Gaussian distributed signals.

Fatigue life prediction of Polymethyl methacrylate (PMMA) polymer under random vibration loading

The objective of this paper is to develop a robust numerical fatigue life prediction model for Polymethyl Methacrylate (PMMA) polymer material of automotive lamp components subjected to random vibration loading, with consideration for material non-linearity to reduce number of iterations in the design cycle. The fatigue life based on initial elastic modulus and secant modulus is predicted using ANSYS software and compared to the experimentally obtained fatigue life. Three fatigue life prediction models, Steinberg, Narrow-Band and Wirsching were used. Twelve specimens cut-out from injection moulded optical blades of PMMA were tested to obtain the fatigue life using electrodynamic shaker. The average experimental fatigue life was obtained from the twelve specimens tested. The use of initial elastic range based modulus gives fatigue life that is 43% lower than the experimental result, while for the secant modulus based analysis, the fatigue life accurately matches the experimental result with only 1% difference. Hence, a complete non-linear finite element model may not be necessary to estimate the fatigue life. The numerical result is based on Wirsching fatigue model, which provides a more accurate prediction than Steinberg and Narrow-Band models.

Implementation of Dirlik’s damage model for the vibration fatigue analysis

Mechanical fatigue is an important phenomenon when the structures are exposed to dynamic, fluctuating loadings. Especially aerospace structures are commonly exposed to random vibration loadings. In this paper, random vibration fatigue is studied both numerically and experimentally. For this purpose, a rectangular cross-section notched beam is designed in order to conduct the vibration fatigue analysis in the frequency domain by the Dirlik’s damage model. Aluminum and steel notched beams are prepared in order to carry out the vibration fatigue tests to compare with the fatigue analysis results. The effect of modal damping on the vibration fatigue analysis results is particularly studied.

Fatigue failure of pb-free electronic packages under random vibration loads

ABSTRACTThe electronic equipment are used in several fields like, automotive, aerospace, consumer goods where they are subjected to vibration loads leading to failure of solder joints used in these equipment. This paper presents a methodology to predict the fatigue life of Pb-free surface mounted BGA packages subjected to random vibrations. The dynamic characteristics of the PCB, such as the natural frequencies, mode shapes and damping ratios were determined. Spectrum analysis was used to determine the stress response of the critical solder joint and the cumulative fatigue damage accumulated by the solder joint for a specific duration was determined.

Modelling of hyperelastic polymers for automotive lamps under random vibration loading with proportional damping for robust fatigue analysis

The objective of this paper was to model random vibration response of components of an automotive lamp made of Polycarbonate/Acrylonitrile Butadiene Styrene (PC-ABS), Polymethyl methacrylate (PMMA) and Polypropylene 40% Talc filled (PPT40) materials using a nonlinear hyperelastic model. Traditionally, the Rayleigh damping matrix used in the dynamic response analysis is constructed considering linear elastic behaviour based on either initial stiffness or secant stiffness. The performance of linear stiffness matrices is compared in this work with that based on the nonlinear hyperelastic, Mooney-Rivlin model, specifically addressing Rayleigh damping matrix construction. The random vibration responses of 10 samples of each material are measured. The mean square error of acceleration response was used to assess the effectiveness. Considering three materials of study, the hyperelastic model resulted in the reduction of the least square error at best by 11.8 times and at worst by 2.6 times. The Mooney-Rivlin material model based Raleigh damping matrix was more accurate in modelling the dynamic behaviour of components of nonlinear materials and it also represented the manufacturing variabilities more reliably.

A Study on Dynamic Amplification Factor and Structure Parameter of Bridge Deck Pavement Based on Bridge Deck Pavement Roughness

In order to study the coupled influence of deck pavement roughness and velocity on dynamic amplification factor, a 2‐DOF 1/4 vehicle model is employed to establish the vehicle‐bridge‐coupled vibration system. The random dynamic load of running vehicle simulated by software MATLAB is applied on bridge deck pavement (BDP) through ANSYS software. Besides, the influence of BDP parameters on control stress under static load and random vibration load is analyzed. The results show that if the surface of BDP is smooth, the dynamic magnification coefficient would first increase and then decrease with increasing of vehicle velocity and reach its maximum value when v = 20 m/s; if the surface of BDP is rough, the maximal and minimum values of the dynamic amplification coefficient (DAC) occur, respectively, when the velocity reaches 10 m/s and 15 m/s. For a composite bridge deck with the cushion layer, the thickness of asphalt pavement should be not too thick or thin and better to be controlled for about 10 cm; with the increasing of cushion layer thickness, the control stress of deck pavement is all decreased and show similar change regularity under effect of different loads. In view of self‐weight of structure, the thickness of the cushion layer is recommended to be controlled for about 4 cm.

Probabilistic fatigue damage estimation of embedded electronic solder joints under random vibration

The stress response to random vibrations is an important factor to be taken into account in designing embedded electronic devices. Several test specifications and qualifications use the random vibrations to increase the reliability of electronic products. Fatigue damage estimation of embedded electronic solder joints has not been addressed, especially under random vibration loading. In this paper numerical random vibration analysis with finite element method of an embedded electronic device is used to estimate the stresses Power Spectral Density (PSD). These PSD of stresses are then used in different probabilistic fatigue damage approaches to estimate the reliability of the solder joints regarding the vibration fatigue damage. Two different probabilistic approaches of random fatigue are employed; the time-domain approach based on Rainflow and Monte Carlo simulations and the frequency domain approach based on spectral techniques and statistical data. However, the fatigue damage estimation depends mainly on the accurate results of the stresses PSD. Thus, this work proposes to develop the sub-modelling technique to the random vibration analysis in order to provide accurate results of the stresses PSD. Moreover, this paper discusses the advantages of the approaches listed above to estimate the fatigue damage in solder joints of an electronic component and shows the effectiveness of sub-modelling techniques in the random vibration analysis.

Effect of Phase angle of Acceleration on Fatigue life in Frequency Domain of Vibration-Based Energy Harvester for Railway vehicle

This study aims to perform fatigue life prediction of vibration-based energy harvester (VEH) considering resonance characteristics. First, we investigated the vibration environment of a structure on which an energy harvester may be installed and determined the level and frequency range of the power spectral density (PSD) exerted on the energy harvester. On the one hand, this research considered random vibration load, because VEH was operated by resonance phenomena. So, to consider random load, life prediction was performed by durability test machine and system. And in order to consider dynamic effect by natural frequency, vibration fatigue analysis was performed in frequency domain. Also, we were performed durability test and vibration fatigue under random load, which is composed of the PSD. As results, accuracy of life prediction procedure for VEH by vibration fatigue analysis was verified.

Fatigue life prediction of Package-on-Package stacking assembly under random vibration loading

This paper presents a general methodology to predict the fatigue life of the Package-on-Package (PoP) under random vibration loading by means of vibration tests and finite element (FE) simulation. The behavior of the critical solder joints of the PoP under vibration loading was accurately described by FE model using ANSYS software and confirmed by modal analysis and linear sweep tests. The stress-life (S-N) curve of the PoP solder joints was obtained by the sinusoidal fatigue vibration tests and FE simulations to characterize the fatigue properties of the PoP under vibration. The comparison of the S-N curves of the SAC305 solder joints in different structures indicates the S-N curve of the SAC305 solder joints depends on the package structure. With the same fatigue cycles, the stress levels for the current 3D package is the smallest compared with the other 2D package due to the stacked structure of the PoP. Spectrum analysis for the random vibration tests was performed by the FE simulations to acquire the stress response power spectral density (PSD) of the critical solder joint. A specific frequency domain approach based on the Palmgren-Miner's rule was established to predict the fatigue life of the PoP under random vibration. Results show that simulated fatigue life matches well with the random vibration test results, which implies that this approach could be a potential method for the predication of fatigue life of the 3D packaging under random vibration.

Accelerated lifetime test of vibration isolator made of Metal Rubber material

The Metal Rubber material (MR) is a kind of material with nonlinear damping characteristics for its application in the field of aerospace, petrochemical industry and so on. The study on the lifetime of MR material is impendent to its application in engineering. Based on the dynamic characteristic of MR, the accelerated lifetime experiments of vibration isolators made of MR working under random vibration load were conducted. The effects of structural parameters of MR components on the lifetime of isolators were studied and modelled with the fitting curves of degradation data. The lifetime prediction methods were proposed based on the models.

Vibratory loads and response prediction for a high-speed flight vehicle during launch events

High-speed flight vehicles (HSFVs) such as space launch vehicles and missiles undergo severe dynamic loads which are generated during the launch and in in-flight environments. A typical vehicle is composed of thin plate skin structures with high-performance electronic units sensitive to such vibratory loads. Such lightweight structures are then exposed to external dynamic loads which consist of random vibration, shock, and acoustic loads created under the operating environment. Three types of dynamic loads (acoustic loads, rocket motor self-induced excitation loads and aerodynamic fluctuating pressure loads) are considered as major components in this study. The estimation results are compared to the design specification (MIL-STD-810) to check the appropriateness. The objective of this paper is to study an estimation methodology which helps to establish design specification for the dynamic loads acting on both vehicle and electronic units at arbitrary locations inside the vehicle.

Verification of MEMS fabrication process for the application of MEMS solid propellant thruster arrays in space through launch and on-orbit environment tests

One of the most significant barriers encountered to the space application of MEMS technology is its lack of reliability and flight heritage in space environments. In this study a MEMS solid propellant thruster array was selected for the verification test of MEMS technology in space. The function and performance of MEMS solid thruster have been previously verified by laboratory-level research in universities. To ensure the successful operation of the MEMS thruster module before flight demonstration on-orbit, launch and on-orbit environment tests were performed at the qualification level. In the launch test, sine burst, and random vibration loads were applied to the MEMS thruster module. The thermal vacuum tests were carried out for the on-orbit environment test. As a result of the launch vibration test and on-orbit environment test, the variations of the characteristics were less than 0.7%, and all the functional requirements were successfully verified after the vibration tests. The tests successfully verified the manufacturing process because the thruster module showed stable normal function before the ignition. The test result outputs will be helpful in establishing MEMS fabrication guidelines for space applications.

Solder material experiencing low temperature inelastic stress and random vibration loading: predicted remaining useful lifetime

Although there exist promising ways to avoid inelastic strains in solder joints of the second level interconnections in IC package designs, it still appears more typical than not that the peripheral joints of a package/PCB assembly experience inelastic strains. This takes place at low temperature conditions, when the deviation from the high fabrication temperature is the largest and the induced thermal stresses are the highest. On the other hand, it is well known that it is the combination of low temperatures and repetitive dynamic loading that accelerate dramatically the propagation of fatigue cracks, whether elastic or inelastic. Accordingly, a modification of the recently suggested Boltzmann–Arrhenius–Zhurkov model is developed for the evaluation of the remaining useful lifetime of the second level solder joint interconnection whose peripheral joints experience inelastic strains. The experimental basis of the approach is the highly focused and highly cost-effective failure-oriented-accelerated-testing (FOAT). The FOAT specimens are subjected in our methodology to the combined action of low temperatures (not to elevated temperatures, as in the classical Arrhenius model) and random vibrations with the given input energy spectrum. The suggested methodology is viewed as a possible, effective and attractive alternative to temperature cycling. As long as inelastic deformations take place, it is assumed that it is these deformations that determine the fatigue lifetime of the solder material, and the state of stress in the elastic mid-portion of the assembly does not have to be accounted for. The roles of the size and stiffness of this mid-portion have to be considered, however, when determining the very existence and establishing the size of the inelastic zones at the peripheral portions of the designs. The general concept is illustrated by a numerical example. Although this example is carried out for a ball-grid-array design, it is applicable to highly popular column-grid-array (CGA) and quad-flat-no-lead (QFN) designs as well. It is noteworthy that it is much easier to avoid inelastic strains in CGA and QFN structures than in the addressed BGA design. The random vibrations are considered in the developed methodology as a white noise of the given (m/s2)2/Hz—the ratio of the acceleration amplitudes squared to the vibration frequency.

Optimal Design for Vibration Reliability of Package-on-Package Assembly Using FEA and Taguchi Method

In this paper, the Taguchi method and finite-element analysis (FEA) were used to improve the vibration reliability of the package-on-package (PoP) assembly and to achieve an optimal design of the PoP under random vibration loading. A finite-element model of the PoP assembly was developed, and experimental modal tests were performed to verify the finite-element model. Four geometry parameters of the PoP were chosen as the variable factors, including body size of PoP, bottom solder joint standoffs, thickness of bottom substrate, and top solder joint standoffs. The volume averaged von Mises stress of the critical solder joint obtained by FEA was chosen as the quality factor, and an $L_{9}$ ( $3^{4})$ orthogonal array was applied for Taguchi experiment to estimate the effects of the four factors and find the optimal design of the PoP on the vibration reliability. It is found that bottom solder joint standoffs have an important effect on the reliability, and more than 36% of the volume averaged Von Mises stress could be reduced by the optimal design.