Showing papers on "Random vibration published in 2010"

Fabrication and characterization of a wideband MEMS energy harvester utilizing nonlinear springs

Abstract: This paper presents the fabrication, characterization and modeling of a wideband MEMS electrostatic energy harvester utilizing nonlinear springs. The experimental results show that the vibration energy harvester displays a strong softening spring effect. For narrow band vibration, the energy harvester exhibits a widening bandwidth during frequency down-sweeps. For increasing levels of broadband random noise vibration, the energy harvester displays a broadening bandwidth response. Furthermore, the vibration energy harvester with softening springs not only increases the bandwidth, but also harvests more output power than a linear energy harvester at a sufficient level of broadband random vibration. At a broadband random vibration of 7.0 × 10−4 g2 Hz−1, we found that the bandwidth increases by more than 13 times and the average harvesting output power increases by 68% compared to that of a linear vibration energy harvester. Numerical analysis confirmed that the softening springs are responsible for the band broadening.

Random Vibration and Spectral Analysis

Abstract: 1. Introduction. 2. Random Variables. 3. Random Processes. 4. Gaussian Process, Poisson Process. 5. Random Response of a Single Degree of Freedom Oscillator. 6. Random Response of Multi Degree of Freedom Systems. 7. Input-Output Relationship for Physical Systems. 8. Spectral Description of Nonstationary Random Processes. 9. Markov Process. 10. Threshold Crossings, Maxima, Envelope and Peak Factor. 11. Random Fatigue. 12. The Discrete Fourier Transform. Bibliography. Index.

The magnetic coupling of a piezoelectric cantilever for enhanced energy harvesting efficiency

Abstract: It is shown that the energy harvesting capabilities of a piezoelectric cantilever can be enhanced through coupling to a static magnetic field. A permanent magnet is fixed to the end of a piezoelectric cantilever, causing it to experience a non-linear force as it moves with respect to a stationary magnet. The magnetically coupled cantilever responds to vibration over a much broader frequency range than a standard cantilever, and exhibits non-periodic or chaotic motion. While the off-resonance response is substantially increased compared to that of a standard cantilever, no reduction in the response at the resonant frequency is observed, as long as a symmetric magnetic force is applied. The magnetically coupled cantilever motion is analyzed using a simple driven harmonic oscillator model with a non-linear magnetic force term. The results show that magnetic coupling can be used to increase the amount of power scavenged from environments containing multi-mode, or random vibration sources.

Steady-State Transverse Response in Coupled Planar Vibration of Axially Moving Viscoelastic Beams

Abstract: Steady-state periodical response is investigated for planar vibration of axially moving viscoelastic beams subjected external transverse loads. A model of the coupled planar vibration is established by introducing a coordinate transform. The model can reduce to two nonlinear models of transverse vibration. The finite difference scheme is developed to calculate steady-state response numerically. Numerical results demonstrate there are steady-state periodic responses in transverse vibration, and resonance occurs if the external load frequency approaches the linear natural frequencies. The effect of material parameters and excitation parameters on the amplitude of the steady-state responses are examined. Numerical results also indicate that the model of coupled vibration and two models of transverse vibration predict qualitatively the same tendencies with the changing parameters, and the two models of transverse vibration yield satisfactory results.

Response in Coupled Planar Vibration of Axially Moving Viscoelastic Beams

Abstract: Steady-state periodical response is investigated for planar vibration of axially moving viscoelastic beams subjected external transverse loads. A model of the coupled planar vibration is established by introducing a coordinate transform. The model can reduce to two nonlinear models of transverse vibration. The finite difference scheme is developed to calculate steady-state response numerically. Numerical results demonstrate there are steady-state periodic responses in transverse vibration, and resonance occurs if the external load frequency approaches the linear natural frequencies. The effect of material parameters and excitation parameters on the amplitude of the steady-state responses are examined. Numerical results also indicate that the model of coupled vibration and two models of transverse vibration predict qualitatively the same tendencies with the changing parameters, and the two models of transverse vibration yield satisfactory results. DOI: 10.1115/1.4000468

Non-stationary random vibration analysis of three dimensional train-bridge systems

Abstract: This paper presents a new non-stationary random vibration technique for the analysis of three-dimensional, time-dependent, train-bridge systems that are subjected to excitations caused by track irregularities. It is based on the pseudo-excitation method (PEM), which was previously applicable only to time-invariant systems, but is extended herein and the result is strictly proven to be applicable to time-dependent systems. The analysis proceeds by taking time lags between the wheel excitations into account, in order that the effects of track irregularity can be regarded as a set of three-dimensional, uniformly modulated, multi-point, different-phase, non-stationary random excitations. This enables the random surface roughness of the track to be transformed using PEM into the superposition of a series of deterministic pseudo-harmonic surface irregularities. The precise integration method is then extended to compute the corresponding pseudo responses. By using these pseudo-responses, various non-stationary random responses, including the time-dependent PSD and RMS of the system, can be obtained conveniently and efficiently. Numerical examples show the effectiveness and accuracy of the present method by comparison with Monte Carlo simulation. Additionally, the characteristics of such non-stationary random responses are discussed.

Harmonic and Random Vibration Durability of SAC305 and Sn37Pb Solder Alloys

Abstract: In this paper, durability tests were conducted on both SAC305 and Sn37Pb solder interconnects using both harmonic and random vibration. The test specimens consist of daisy-chained printed wiring boards (PWBs) with several different surface-mount component styles. Modal testing was first conducted on a test PWB to determine the natural frequencies and mode shapes. The PWB was then subjected to narrow-band excitation at its first natural frequency. Electrical continuity of the daisy-chain nets was monitored to measure the time-to-failure (and hence cycles-to-failure) of the interconnects. The response history of the PWB was recorded with strain gages located near the components of interest. Finite element analysis (FEA) was conducted for each component type, to estimate the transfer function between the flexural strain of the PWB and the strain in the critical solder joint. The predicted strain transfer function was then combined with the measured PWB strain response history to estimate the strain history in the critical solder joints. The solder strain history was used, in conjunction with the failure history, to estimate lower bounds for the fatigue durability (S-N curves) of the solder interconnects. In the first part of this paper, the results show that the SAC305 interconnects are marginally less durable than Sn37Pb interconnects for the harmonic excitation range used in this paper. The durability model constants are found to be very sensitive to the solder stress-strain curve assumed in the FEA. Since the stress-strain properties reported in the literature for these solder alloys vary significantly, the solder stress-strain curves were parametrically varied in the FEA, to assess the resulting effect on the estimated S-N curves. In the second part of this paper, random-vibration tests were conducted to assess durability under step-stress, broad-band excitation. Conventional cycle counting techniques were used to quantify the random excitation histories in terms of range distribution functions. Using the same time-domain vibration fatigue analysis used earlier for narrow-band excitation, the durability trend for the corresponding SAC305 and Sn37Pb solder interconnects under broad-band excitation was found to be similar to that found earlier under harmonic vibration excitation. Comparison between the durability prediction and test results provides a good understanding of the effect of stress-strain behavior on the fatigue constants of these solder materials. The best set of material properties was then used to verify the durability of leadless chip resistor interconnects under quasi-static mechanical cycling.

Enhancement of Energy Harvested from a Random Vibration Source by Magnetic Coupling of a Piezoelectric Cantilever

Abstract: It is demonstrated experimentally that the energy harvested from a random noise source by a piezoelectric cantilever can be substantially enhanced by introducing a magnetic coupling force. The coupled cantilever responds to a 1/f vibration spectrum (‘pink noise’) with chaotic motion that on average has larger amplitude than the non-chaotic motion of an uncoupled cantilever. A 50% increase in output voltage was observed in the coupled cantilever compared to the uncoupled cantilever. Calculations show that the magnetic force transforms the quadratic spring potential of the cantilever into a double valley of two potential wells. Fluctuations between the two potential minima increase the amplitude of the cantilever motion over a range of vibration frequencies.

Prediction of Extreme Response Statistics of Narrow-Band Random Vibrations

Abstract: The paper focuses on the development of a general method for extreme response estimation of dynamical systems subjected to random excitations. One of the most important elements in structural safety is an assessment of the exceedance or failure probability. The frequently used Poisson assumption tends to overestimate the exceedance level if the response spectrum has narrow-banded features since the so-called clustering effects occur. The latter inaccuracy may be corrected by using an alternative approach studied in this paper, which enables accurate prediction of extremes irrespective of clustering effects.

Biodynamic responses of the seated human body to single-axis and dual-axis vibration.

Abstract: Occupational exposures to vibration always involve multi-axis vibration. Since human responses to vibration are highly nonlinear and cross-coupled, it is to be expected that excitation in one axis will alter response to vibration in another axis. The purpose of this study was to investigate nonlinearity in the apparent masses of subjects seated without a backrest and exposed to single-axis and dual-axis vertical and fore-and-aft excitation. The driving point apparent masses and cross-axis apparent masses in the two translational directions were measured with twelve subjects exposed to random vibration (0.2 to 20 Hz) in all 15 possible combinations of four vibration magnitudes (0, 0.25, 0.5, or 1.0 ms–2 r.m.s.) in the fore-and-aft and vertical directions. With single-axis excitation (either fore-and-aft or vertical), the median in-line apparent mass exhibited a nonlinear characteristic in which the body softened with increasing magnitude of vibration. With dual-axis excitation, at all magnitudes of vertical excitation the resonance frequency in the vertical apparent mass reduced as the magnitude of fore-and-aft vibration increased, and at all except the greatest magnitude of fore-andaft excitation the resonance frequency in the fore-and-aft apparent mass reduced as the magnitude of vertical vibration increased. The coherency between the fore-and-aft acceleration and the fore-and-aft force was lowered by the addition of vertical excitation, and the coherency between the vertical acceleration and the vertical force was lowered by the addition of fore-and-aft excitation. The nonlinearity evident in both in-line apparent masses was also evident in the crossaxis apparent masses. It is concluded that with dual-axis excitation the fore-and-aft and vertical response of the seated human body is nonlinear, with resonance frequencies decreasing with increasing magnitude of vibration. Consequently, vibration in one axis (either fore-and-aft or vertical) affects the apparent mass of the body measured in the other axis (either vertical or fore-and-aft).

Modeling and Control of Vibration in Mechanical Systems

Abstract: Many chapters have introductions, conclusions, and references Symbols and Acronyms 1 Mechanical Systems and Vibration Magnetic recording system Stewart platform Vibration sources and descriptions Types of vibration Random vibration Vibration analysis 2 Modeling of Disk Drive System and Its Vibration Introduction System description System modeling Vibration modeling Modeling of Stewart Platform System description and governing equations Modeling using adaptive filtering approach Classical Vibration Control Passive control Self-adapting systems Active vibration control Introduction to Optimal and Robust Control H2 and H norms H2 optimal control H control Robust control Controller parametrization Performance limitation Mixed H2/H Control Design for Vibration Rejection Mixed H2/H control problem Method 1: slack variable approach Method 2: an improved slack variable approach Application in servo loop design for hard disk drives Low-Hump Sensitivity Control Design for Hard Disk Drive Systems Problem statement Design in continuous-time domain Design in discrete-time domain Generalized KYP Lemma-Based Loop Shaping Control Design Problem description Generalized KYP lemma-based control design method Peak filter Application in high frequency vibration rejection Application in mid-frequency vibration rejection Combined H2 and KYP Lemma-Based Control Design Problem formulation Controller design for specific disturbance rejection and overall error minimization Simulation and implementation results Blending Control forMulti-Frequency Disturbance Rejection Control blending Control blending application in multi-frequency disturbance rejection Simulation and experimental results H -Based Design for Disturbance Observer Conventional disturbance observer A general form of disturbance observer Application results Two-DimensionalH2 Control for Error Minimization 2-D stabilization control 2-D H2 control SSTW process and modeling Feedforward compensation method 2-D control formulation for SSTW 2-D stabilization control for error propagation containment 2-D H2 control for error minimization Nonlinearity Compensation and Nonlinear Control Nonlinearity compensation Nonlinear control Quantization Effect on Vibration Rejection and Its Compensation Description of control system with quantizer Quantization effect on error rejection Compensation of quantization effect on error rejectioAdaptive Filtering Algorithms for Active Vibration Control Adaptive feedforward algorithm Adaptive feedback algorithm Comparison between feedforward and feedback controls Application in Stewart platform

Random Vibrations in Space Structures Design¿Theory and Applications

Abstract: Random Mechanical Vibration.- Linear Random Vibration Systems.- Acoustic Random Vibration.- Low Frequency Acoustic Loads.- Statistical Energy Analysis.- Statistical Energy Analysis.- Fokker-Planck-Kolmogorov Method or Diffusion Equation Method.- Fokker-Planck-Kolmogorov Method or Diffusion Equation Method.

On Magnetorheologic Elastomers for Vibration Isolation, Damping, and Stress Reduction in Mass-varying Structures

Abstract: This article considers two devices based on a magnetorheological elastomer (MRE): an MRE isolator under a frequency-varying harmonic excitation and a MRE Dynamic Vibration Absorber (DVA) mounted on a frequency-varying structure under a random excitation. In the first case, it is shown that the commandability of the elastomer improves the reduction of the RMS value of the body displacement by 10%. In the second case, it is shown on a simple example that a MRE DVA, while not optimal, can reduce the stress in the structure about 50% better than a classical DVA when the mass of the structure changes 35%. This makes them suitable to avoid high stress in mass-varying structures, and delay some damage mechanisms like the emergence of cracks and fatigue.

Finite element based fatigue life prediction for electronic components under random vibration loading

Abstract: This work develops an assessment methodology based on experiments and finite element analysis (FEA) to determine the solder joint fatigue life of electronic components under random vibration loading. Specially designed PCB with Ball Grid Array (BGA) packages attached was mounted to the Electro dynamic shaker and was applied to different random vibration excitations at the supports. Meanwhile, an event detector monitored the resistance of the daisy chained circuits and recorded the failure time of the electronic components. In addition accelerometers and dynamic signal analyzer were utilized to record the time history data of both the shaker input and the PCB's response, and to obtain the transmissibility function of the test vehicles. This finite element based fatigue life prediction approach consists of two steps: The first step aims at characterizing fatigue properties of the solder joint by generating its own S-N (stress-life) curve. A sinusoidal vibration over a limited frequency band centered at the test vehicle's 1st natural frequency was applied and the time to failure was recorded. The resulting stress was obtained from the FE model through harmonic analysis in ANSYS. Spectrum analysis specified for random vibration, as the second step, was performed numerically in ANSYS to obtain the response Power Spectral Density (PSD) of the critical solder ball. The volume averaged Von Mises stress PSD was calculated out of the FEA results and then was transformed into time history data through inverse Fourier transform. Rainflow cycle counting was used to estimate cumulative damage of the critical solder joint. The calculated fatigue life based on the Rainflow cycle counting results, the S-N curve, and the modified Miner's rule agreed with actual testing results.

Linear random vibration by stochastic reduced-order models

Abstract: A practical method is developed for calculating statistics of the states of linear dynamic systems with deterministic properties subjected to non-Gaussian noise and systems with uncertain properties subjected to Gaussian and non-Gaussian noise. These classes of problems are relevant as most systems have uncertain properties, physical noise is rarely Gaussian, and the classical theory of linear random vibration applies to deterministic systems and can only deliver the first two moments of a system state if the noise is non-Gaussian. The method (1) is based on approximate representations of all or some of the random elements in the definition of linear random vibration problems by stochastic reduced-order models (SROMs), that is, simple random elements having a finite number of outcomes of unequal probabilities, (2) can be used to calculate statistics of a system state beyond its first two moments, and (3) establishes bounds on the discrepancy between exact and SROM-based solutions of linear random vibration problems. The implementation of the method has required to integrate existing and new numerical algorithms. Examples are presented to illustrate the application of the proposed method and assess its accuracy. Copyright © 2009 John Wiley & Sons, Ltd.

Effects of horizontal whole-body vibration and standing posture on activity interference

Abstract: Standing people are exposed to whole-body vibration in many environments. This paper investigates the effects of horizontal whole-body vibration and standing posture on task performance. Sixteen participants were exposed to random vibration (up to 4 Hz) whilst performing a timed pegboard task in two standing postures. Objective and subjective indicators of performance were used. Time taken to complete the task increased progressively with increases in vibration magnitude. The fore-and-aft posture generally showed greater performance decrements and postural interruptions (>1.0 ms(-2) root mean square) than the lateral. For both postures, performance was better during y-axis vibration than during x-axis vibration. Subjective ratings showed similar trends to time data. Impairments due to dual axis exposure were well predicted using root sum of squares calculations based on single axis components. These results indicate that best performance for those standing in moving environments will be achieved if individuals adopt a lateral posture with the most severe vibration in the y-axis. STATEMENT OF RELEVANCE: People have a need to work during transportation, either working for the transport provider or as a passenger. All modes of transport result in travellers being exposed to horizontal motion. This study demonstrates that task disturbance is affected by the orientation of the standing person to the vibration and, therefore, vehicle layouts can be optimised.