Random Vibration of Diamond-Beaded Rope Subject to a Concentrated Load

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Fei Wang ◽  
Jinsheng Zhang ◽  
Bo Huang ◽  
Zhi Wang ◽  
Jingkun Wang
Keyword(s):  
Random Vibration ◽  
Lateral Displacement ◽  
Vibration Characteristics ◽  
Transverse Displacement ◽  
Mean Square ◽  
Concentrated Load ◽  
Sawing Force ◽  
Load Response ◽  
Power Spectral ◽  
The Mean

In this work, the random vibration characteristics of a beaded rope under a concentrated load are investigated. A stochastic model describing the sawing force of a single diamond-beaded rope was established, based on the principle of volume invariability. The governing equations of the beaded rope were obtained using Hamilton's principle. Theoretical expressions were derived to calculate the response power spectral density (PSD), load-response cross-PSD and the mean square value of the beaded rope lateral displacement, for a beaded rope subject to a concentrated load. The influence of the parameters on the random vibration characteristics of a beaded rope was analyzed, including the effects of the linear speed of the beaded rope, the tension of the beaded rope, and the location of the concentrated load. Numerical examples are given. Results show that as the tension of the beaded rope increases, the PSD and mean square value of the rope displacement are reduced. However, as the linear velocity of the beaded rope increases, the PSD and mean square value of the rope displacement are also increased. During movement of the diamond-beaded rope, the mean square value of the transverse displacement fluctuates predominantly, because of the time-varying impact force caused by the diamond beads.

Stationary random vibration of a viscoelastic Timoshenko cantilever beam under diverse random processes

2019 ◽  
Vol 234 (4) ◽  
pp. 849-861
Author(s):  
Qingzhao Zhou ◽  
David He ◽  
Yaping Zhao
Keyword(s):  
White Noise ◽  
Cantilever Beam ◽  
Time Correlation ◽  
Random Excitation ◽  
Transverse Displacement ◽  
Mean Square ◽  
Concentrated Force ◽  
The Mean ◽  
Definite Integration ◽  
Band Limited

In this paper, the stochastic properties of a uniform Timoshenko cantilever beam are investigated systematically. Based on the external viscous damping and Kelvin–Voigt viscoelastic damping, the partial differential equations of the Timoshenko beam subjected to random excitation are derived. The applied load is the concentrated force, and the excitation related to includes the ideal white noise, the band-limited white noise, and the exponential noise. Expressions are obtained for the space–time correlation functions and the space–frequency power spectral density functions of the transverse displacement response. The evident improvement is that the infinite integral and the definite integration in the mean square responses are worked out by means of the residue integral method and the integration by partial fraction, and the exact solutions of the mean square response are obtained in the form of an infinite series finally. This improvement provides a basis for both the mode truncation and the modal cross-spectral densities whether which can be ignored. Providing the numerical example, the numerical results obtained show the effectiveness of the theoretical analysis.

Optimal Wiener Filter for a Body Mounted Inertial Attitude Sensor

2008 ◽  
Vol 61 (3) ◽  
pp. 455-472 ◽  
Author(s):  
Peter Rizun
Keyword(s):  
Spectral Density ◽  
White Noise ◽  
Power Spectral Density ◽  
Human Body ◽  
Linear Acceleration ◽  
Mean Square ◽  
White Noise Process ◽  
Noise Process ◽  
Power Spectral ◽  
The Mean

An optimal attitude estimator is presented for a human body-mounted inertial measurement unit employing orthogonal triads of gyroscopes, accelerometers and magnetometers. The estimator continuously fuses gyroscope and accelerometer measurements together in a manner that minimizes the mean square error in the estimate of the gravity vector, based on known spectral characteristics for the gyroscope noise and the linear acceleration of points on the human body. The gyroscope noise is modelled as a white noise process of power spectral density δn2/2 while the linear acceleration is modelled as the derivative of a band-limited white noise process of power spectral density δv2/2. The estimator is robust to centripetal acceleration and guaranteed to have zero mean error regardless of the motion of the sensor. The mean square angular error in attitude is shown to be independent of the module's angular velocity and equal to 21/2g−1/2δn3/2δv1/2.

Random vibration energy harvesting on thin plates using multiple piezopatches

2016 ◽  
Vol 27 (20) ◽  
pp. 2744-2756 ◽  
Author(s):  
Ugur Aridogan ◽  
Ipek Basdogan ◽  
Alper Erturk
Keyword(s):  
Energy Harvesting ◽  
Random Vibration ◽  
Numerical Solutions ◽  
Thin Plates ◽  
Experimental Measurements ◽  
Mean Square ◽  
Mean Power ◽  
Piezoelectric Cantilever ◽  
The Mean ◽  
Mean Power Output

Vibrational energy harvesting using piezoelectric cantilever beams has received significant attention over the past decade. When compared to piezoelectric cantilever-based harvesters, piezopatch energy harvesters integrated on plate-like thin structures can be a more efficient and compact option to supply electrical power for wireless structural health and condition monitoring systems. In this article, electroelastic modeling, analytical and numerical solutions, and experimental validations of piezopatch-based energy harvesting from stationary random vibrations of thin plates are presented. Electroelastic models for the series and parallel connected multiple piezopatches are given based on a distributed-parameter modeling approach for a thin host plate excited by a transverse point force. The analytical and numerical solutions for the mean power output and the mean-square shunted vibration response are then derived. The experimental measurements are carried out by employing a fully clamped thin plate with three piezopatches connected in series. It is shown that the analytical and numerical model predictions for the mean power output and the mean-square velocity response are in very good agreement with the experimental measurements. The electroelastic modeling framework and solution methods presented in this work can be used for design, performance analysis, and optimization of piezoelectric energy harvesting from stationary random vibration of thin plates.

Comparing Random Vibration Inputs: Power Spectral Density (PSD) Versus Root Mean-Square Acceleration (Grms)

2003 ◽  
Author(s):  
Ivan Straznicky
Keyword(s):  
Spectral Density ◽  
Root Mean Square ◽  
Power Spectral Density ◽  
Fatigue Damage ◽  
Random Vibration ◽  
Mean Square ◽  
Vibration Effect ◽  
Operating Environments ◽  
Power Spectral ◽  
Magnitude Difference

Many defense programs have vibration requirements for electronics which are often specified as random vibration input. Often, this input is based on measurements taken at the locations of interest for the spectrum of vehicle operating environments. The resulting specification is typically several power spectral density, or PSD, curves with associated durations. The root mean square acceleration, or Grms, can be readily calculated for each PSD curve. Grms values are sometimes used to compare different PSD curves for severity. However, this can be misleading. The impacts of two different random vibration inputs, with the same Grms value, can be very different. By calculating fatigue damage values for various components on a circuit card assembly subjected to these inputs, it can be shown that equal Grms values do not result in equal damage. In fact, there can be two orders of magnitude difference in component damage values. This means that Grms values are very poor indicators of random vibration effect, and should not be used for comparison purposes.

A Closure Procedure for Random Vibration Parametric Resonances

2005 ◽  
Vol 11 (2) ◽  
pp. 215-223 ◽  
Author(s):  
R. V. Bobryk ◽  
A. Chrzeszczyk ◽  
L. Stettner
Keyword(s):  
Random Vibration ◽  
Large Scale ◽  
Narrow Band ◽  
Numerical Approach ◽  
Mean Square ◽  
Moment Equations ◽  
Single Degree Of Freedom ◽  
Mean Square Stability ◽  
Parametric Resonances ◽  
The Mean

We investigate the mean-square stability for single-degree-of-freedom linear systems with random parametric excitation. The excitation is assumed to be of the form of a Gaussian stationary non-white process. We propose a new numerical approach to determine regions of parametric resonances based on a closure procedure for hierarchy of moment equations. Mean-square stability charts are obtained using the numerical analysis of eigenvalues for large-scale matrices. The results show three parametric resonances for narrow-band excitations.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

The mean-square generalized delayed decision feedback sequence detector

2003 ◽  
Vol 14 (3) ◽  
pp. 265-268 ◽  
Author(s):  
Maurizio Magarini ◽  
Arnaldo Spalvieri ◽  
Guido Tartara
Keyword(s):  
Decision Feedback ◽  
Mean Square ◽  
The Mean

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

scholarly journals Electrical stimulator with mechanomyography-based real-time monitoring, muscle fatigue detection, and safety shut-off: a pilot study

2020 ◽  
Vol 65 (4) ◽  
pp. 461-468
Author(s):  
Jannatul Naeem ◽  
Nur Azah Hamzaid ◽  
Amelia Wong Azman ◽  
Manfred Bijak
Keyword(s):  
Muscle Fatigue ◽  
Real Time ◽  
Isometric Force ◽  
Mean Square ◽  
Clear Indication ◽  
Initial Value ◽  
Cord Injury ◽  
The Mean ◽  
Electrical Stimulator ◽  
Fatigue Detection

AbstractFunctional electrical stimulation (FES) has been used to produce force-related activities on the paralyzed muscle among spinal cord injury (SCI) individuals. Early muscle fatigue is an issue in all FES applications. If not properly monitored, overstimulation can occur, which can lead to muscle damage. A real-time mechanomyography (MMG)-based FES system was implemented on the quadriceps muscles of three individuals with SCI to generate an isometric force on both legs. Three threshold drop levels of MMG-root mean square (MMG-RMS) feature (thr50, thr60, and thr70; representing 50%, 60%, and 70% drop from initial MMG-RMS values, respectively) were used to terminate the stimulation session. The mean stimulation time increased when the MMG-RMS drop threshold increased (thr50: 22.7 s, thr60: 25.7 s, and thr70: 27.3 s), indicating longer sessions when lower performance drop was allowed. Moreover, at thr70, the torque dropped below 50% from the initial value in 14 trials, more than at thr50 and thr60. This is a clear indication of muscle fatigue detection using the MMG-RMS value. The stimulation time at thr70 was significantly longer (p = 0.013) than that at thr50. The results demonstrated that a real-time MMG-based FES monitoring system has the potential to prevent the onset of critical muscle fatigue in individuals with SCI in prolonged FES sessions.

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