Analytical Solutions of Bimodal Gaussian Processes’ Fatigue Damages

2017 ◽  
Author(s):  
Wenbo Huang
Keyword(s):  
Analytical Solutions ◽  
Gaussian Processes ◽  
High Frequency ◽  
Numerical Solutions ◽  
Low Frequency ◽  
Frequency Domain Method ◽  
Load Combination ◽  
Analytical Formulas ◽  
Reduction Effect ◽  
Damage Estimates

Based on the rain-flow counting technique, a frequency domain method is developed for calculating the fatigue damages caused by the bimodal Gaussian loads. Firstly, by considering the reduction effect of low frequency loads on high frequency ones, the amplitudes of the small rain-flow cycles are obtained. Secondly, the amplitudes of the large rain-flow cycles are determined by means of Turkstra’s rule of load combination. Moreover, based on the numerical solutions developed, the two analytical formulas for the damage estimates of small and large cycles are developed. Both numerical and analytical solutions are benchmarked against the rain-flow damage estimates and compared with the existing ones. The numerical analyses show that the damages estimated by the new method are close to the rain-flow damages.

Fatigue of Combined Drag and Inertial Forces

2014 ◽  
Author(s):  
Wenbo Huang
Keyword(s):  
Numerical Analysis ◽  
Fatigue Damage ◽  
High Frequency ◽  
Low Frequency ◽  
Inertial Force ◽  
Frequency Domain Method ◽  
Inertial Forces ◽  
Combined Load ◽  
Drag Forces ◽  
Load Combination

Based on the rain-flow counting technique, a frequency domain method is developed for calculating the fatigue damage caused by the combined drag and inertial loads. Firstly, by observation of the combined signal simulated, the combined load can be considered as the oscillation of the high frequency inertial force around the low frequency drag force with the random amplitudes, which makes it possible to identify the rain-flow large and small cycles. The cyclic range of rain-flow small cycles are determined by considering the reduced effect of the low frequency drag forces on the cyclic range of high frequency inertial forces. The cyclic ranges of rain-flow large cycles are determined by means of Turkstra’s rule of load combination. The numerical analysis show that the damages estimated by the developed method are very close to the rain-flow damages.

Effects of averaging and sampling on the statistics of reflection coefficients

Geophysics ◽  
1991 ◽  
Vol 56 (1) ◽  
pp. 50-58 ◽  
Author(s):  
K. Hsu ◽  
R. Burridge
Keyword(s):  
Reflection Coefficient ◽  
High Frequency ◽  
Low Frequency ◽  
Seismic Exploration ◽  
Reflection Coefficients ◽  
Continuous Formation ◽  
Sampling Intervals ◽  
Frequency Components ◽  
Analytical Formulas

The reflection coefficients derived from sonic and density logs are frequently used in seismic exploration. Even though they measure the in‐situ formation slowness and density, sonic and density tools do not measure the exact, continuous formation properties but locally averaged properties sampled at discrete depth points. Furthermore, the logs are frequently reinterpolated to form a Goupillaud medium for many applications such as synthetic seismogram computation. Both the logging tools and the Goupillaud interpolation introduce averaging and sampling effects into the reflection coefficients and significantly alter the autocorrelation of the reflection coefficient sequence. Analytical formulas are derived to show how the autocorrelation is altered and to calculate how the autocorrelation depends on the averaging and sampling intervals. Essentially, these effects impose sincsquared envelopes on the power spectrum of the reflection coefficient sequence and alias high‐frequency components to low‐frequency components in the spectral domain. These findings are verified using synthetic and real examples.

Progress in Analytical Modeling of Water Hammer

2021 ◽  
Author(s):  
Kamil Urbanowicz ◽  
Haixiao Jing ◽  
Anton Bergant ◽  
Michał Stosiak ◽  
Marek Lubecki
Keyword(s):  
Analytical Solutions ◽  
Numerical Solutions ◽  
Dynamic Pressure ◽  
Complete Solution ◽  
Water Hammer ◽  
Inverse Transformation ◽  
Mathematical Form ◽  
Dimensionless Time ◽  
Wide Range ◽  
Analytical Formulas

Abstract In this paper analytical formulas of water hammer known from the literature are simplified to the shortest possible mathematical form based on dimensionless parameters: dimensionless time, water hammer number, etc. Novel formulas are determined, for example for the flow velocity and wall shear stress in the Muto and Takahashi solution. A complete solution in the Laplace domain is presented and the problem of its inverse transformation is discussed. A series of comparative studies of analytical solutions with numerical solutions and the results of experimental research were carried out. The compared analytical solutions, taking into account the frequency-dependent nature of the hydraulic resistances, show very good agreement with the experimental results in a wide range of water hammer numbers, in particular when Wh ≤ 0.1. On the other hand, it turned out that the analytical model based on the quasi-steady friction in great detail simulates dynamic pressure response in systems characterized by a high value of the water hammer number Wh ≥ 0.5.

scholarly journals Local predictability in a simple model of atmospheric balance

2003 ◽  
Vol 10 (3) ◽  
pp. 183-196 ◽  
Author(s):  
G. Gyarmati ◽  
I. Szunyogh ◽  
D. J. Patil
Keyword(s):  
High Frequency ◽  
Numerical Solutions ◽  
Coupling Parameter ◽  
Low Frequency ◽  
Singular Value ◽  
Pendulum Equation ◽  
Single Coupling ◽  
High Frequency Waves ◽  
Balanced Dynamics ◽  
Elastic Pendulum

Abstract. The 2 degree-of-freedom elastic pendulum equations can be considered as the lowest order analogue of interacting low-frequency (slow) Rossby-Haurwitz and high-frequency (fast) gravity waves in the atmosphere. The strength of the coupling between the low and the high frequency waves is controlled by a single coupling parameter, e, defined by the ratio of the fast and slow characteristic time scales. In this paper, efficient, high accuracy, and symplectic structure preserving numerical solutions are designed for the elastic pendulum equation in order to study the role balanced dynamics play in local predictability. To quantify changes in the local predictability, two measures are considered: the local Lyapunov number and the leading singular value of the tangent linear map. It is shown, both based on theoretical considerations and numerical experiments, that there exist regions of the phase space where the local Lyapunov number indicates exceptionally high predictability, while the dominant singular value indicates exceptionally low predictability. It is also demonstrated that the local Lyapunov number has a tendency to choose instabilities associated with balanced motions, while the dominant singular value favors instabilities related to highly unbalanced motions. The implications of these findings for atmospheric dynamics are also discussed.

Simulations of high-resolution images of amorphous silicon films

1986 ◽  
Vol 44 ◽  
pp. 544-545
Author(s):  
G. Y. Fan ◽  
J. M. Cowley
Keyword(s):  
Electron Microscope ◽  
High Frequency ◽  
Fourier Transformation ◽  
Amorphous Materials ◽  
Low Frequency ◽  
Chromatic Aberration ◽  
Structure Information ◽  
Frequency Components ◽  
High Resolution Images ◽  
Spatial Frequency Spectrum

It is well known that the structure information on the specimen is not always faithfully transferred through the electron microscope. Firstly, the spatial frequency spectrum is modulated by the transfer function (TF) at the focal plane. Secondly, the spectrum suffers high frequency cut-off by the aperture (or effectively damping terms such as chromatic aberration). While these do not have essential effect on imaging crystal periodicity as long as the low order Bragg spots are inside the aperture, although the contrast may be reversed, they may change the appearance of images of amorphous materials completely. Because the spectrum of amorphous materials is continuous, modulation of it emphasizes some components while weakening others. Especially the cut-off of high frequency components, which contribute to amorphous image just as strongly as low frequency components can have a fundamental effect. This can be illustrated through computer simulation. Imaging of a whitenoise object with an electron microscope without TF limitation gives Fig. 1a, which is obtained by Fourier transformation of a constant amplitude combined with random phases generated by computer.

SEM image sharpness analysis

1996 ◽  
Vol 54 ◽  
pp. 142-143
Author(s):  
M. T. Postek ◽  
A. E. Vladar
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Quantitative Information ◽  
Primary Electron ◽  
Image Sharpness ◽  
Critical Dimensions ◽  
Sem Image ◽  
Frequency Changes ◽  
Electron Microscopes ◽  
Scanning Electron

Fully automated or semi-automated scanning electron microscopes (SEM) are now commonly used in semiconductor production and other forms of manufacturing. The industry requires that an automated instrument must be routinely capable of 5 nm resolution (or better) at 1.0 kV accelerating voltage for the measurement of nominal 0.25-0.35 micrometer semiconductor critical dimensions. Testing and proving that the instrument is performing at this level on a day-by-day basis is an industry need and concern which has been the object of a study at NIST and the fundamentals and results are discussed in this paper.In scanning electron microscopy, two of the most important instrument parameters are the size and shape of the primary electron beam and any image taken in a scanning electron microscope is the result of the sample and electron probe interaction. The low frequency changes in the video signal, collected from the sample, contains information about the larger features and the high frequency changes carry information of finer details. The sharper the image, the larger the number of high frequency components making up that image. Fast Fourier Transform (FFT) analysis of an SEM image can be employed to provide qualitiative and ultimately quantitative information regarding the SEM image quality.

Real Ear Sound Pressure Levels Developed by Three Portable Stereo System Earphones

1992 ◽  
Vol 1 (4) ◽  
pp. 52-55 ◽  
Author(s):  
Gail L. MacLean ◽  
Andrew Stuart ◽  
Robert Stenstrom
Keyword(s):  
High Frequency ◽  
Sound Pressure ◽  
Low Frequency ◽  
Test System ◽  
Output Frequency ◽  
Frequency Effects ◽  
Adult Men ◽  
Frequency Responses ◽  
Significant Difference ◽  
Sound Pressure Levels

Differences in real ear sound pressure levels (SPLs) with three portable stereo system (PSS) earphones (supraaural [Sony Model MDR-44], semiaural [Sony Model MDR-A15L], and insert [Sony Model MDR-E225]) were investigated. Twelve adult men served as subjects. Frequency response, high frequency average (HFA) output, peak output, peak output frequency, and overall RMS output for each PSS earphone were obtained with a probe tube microphone system (Fonix 6500 Hearing Aid Test System). Results indicated a significant difference in mean RMS outputs with nonsignificant differences in mean HFA outputs, peak outputs, and peak output frequencies among PSS earphones. Differences in mean overall RMS outputs were attributed to differences in low-frequency effects that were observed among the frequency responses of the three PSS earphones. It is suggested that one cannot assume equivalent real ear SPLs, with equivalent inputs, among different styles of PSS earphones.

Evaluation of Special Hearing Aids for Deaf Children

1971 ◽  
Vol 36 (4) ◽  
pp. 527-537 ◽  
Author(s):  
Norman P. Erber
Keyword(s):  
Hearing Aids ◽  
High Frequency ◽  
Hearing Aid ◽  
Low Frequency ◽  
Acoustic Stimulation ◽  
Deaf Children ◽  
Frequency Range ◽  
Frequency Limit ◽  
Unpublished Studies ◽  
Published Research

Two types of special hearing aid have been developed recently to improve the reception of speech by profoundly deaf children. In a different way, each special system provides greater low-frequency acoustic stimulation to deaf ears than does a conventional hearing aid. One of the devices extends the low-frequency limit of amplification; the other shifts high-frequency energy to a lower frequency range. In general, previous evaluations of these special hearing aids have obtained inconsistent or inconclusive results. This paper reviews most of the published research on the use of special hearing aids by deaf children, summarizes several unpublished studies, and suggests a set of guidelines for future evaluations of special and conventional amplification systems.

Efeitos do Método Pilates sobre a variabilidade da frequência cardíaca, flexibilidade e variáveis antropométricas em indivíduos sedentários

2016 ◽  
Vol 17 (1) ◽  
pp. 66
Author(s):  
Maria Lina Silva Leite
Keyword(s):  
High Frequency ◽  
Low Frequency

O objetivo deste estudo foi avaliar os efeitos do Método Pilates sobre a variabilidade da frequência cardíaca, na flexibilidade e nas variáveis antropométricas em indivíduos sedentários. O presente estudo contou com 14 voluntárias do sexo feminino, na faixa etária entre 40 e 55 anos, que realizaram 20 sessões de exercícios do Método Pilates, duas vezes por semana, com duração de 45 minutos cada sessão, dividida em três fases: repouso, exercício e recuperação. As variáveis estudadas foram: os dados antropométricos, flexibilidade avaliada utilizando o teste de sentar-e-alcançar com o Banco de Wells, e intervalos R-R usando um cardiotacômetro. O processamento dos sinais da frequência cardíaca foi efetuado em ambiente MatLab 6.1®, utilizando a TWC. Os dados coletados foram submetidos ao teste de normalidade de Shapiro Wilk e foi utilizado o teste de Wilcoxon e Anova One Way (α = 0,05). Nos resultados, observou-se que não houve diferenças significativas entre os valores antropométricos e de frequência cardíaca, porém houve aumento da flexibilidade com o treinamento. Comparando a primeira e a vigésima sessão com relação aos parâmetros low frequency (LF), high frequency (HF), e relação LF/HF, não houve diferença na fase de repouso e foram constatadas diferenças significativas de LF (p = 0,04) e HF (p = 0,04) na fase de exercício e diferença significativa de LF/HF (p = 0,05) na fase de recuperação. Comparando os parâmetros nos períodos de repouso, exercícios e recuperação durante a primeira sessão e durante a vigésima sessão, não houve diferença significativa nos parâmetros LF, HF e LF/HF. Pode-se concluir que, em relação à flexibilidade, foi observada uma melhora significativa, enquanto a análise da frequência cardíaca caracterizou a intensidade do exercício de 50% da capacidade funcional das voluntárias. Em relação aos parâmetros LF, HF e LF/HF foram observados um aumento da variabilidade da frequência cardíaca, provavelmente produto da atividade do Método Pilates. A Transformada Wavelet (TWC) mostrou-se um Método adequado para as análises da variabilidade da frequência cardíaca.Palavras-chave: frequência cardíaca, Transformada Wavelet, Pilates.

Dynamics of the processes in metal machining

1998 ◽  
Vol 2 ◽  
pp. 115-122
Author(s):  
Donatas Švitra ◽  
Jolanta Janutėnienė
Keyword(s):  
High Frequency ◽  
Machine Tools ◽  
Metal Cutting ◽  
Cutting Tool ◽  
Low Frequency ◽  
Metal Cutting Machine ◽  
Cutting Machine ◽  
Metal Machining

In the practice of processing of metals by cutting it is necessary to overcome the vibration of the cutting tool, the processed detail and units of the machine tool. These vibrations in many cases are an obstacle to increase the productivity and quality of treatment of details on metal-cutting machine tools. Vibration at cutting of metals is a very diverse phenomenon due to both it’s nature and the form of oscillatory motion. The most general classification of vibrations at cutting is a division them into forced vibration and autovibrations. The most difficult to remove and poorly investigated are the autovibrations, i.e. vibrations arising at the absence of external periodic forces. The autovibrations, stipulated by the process of cutting on metalcutting machine are of two types: the low-frequency autovibrations and high-frequency autovibrations. When the low-frequency autovibration there appear, the cutting process ought to be terminated and the cause of the vibrations eliminated. Otherwise, there is a danger of a break of both machine and tool. In the case of high-frequency vibration the machine operates apparently quiently, but the processed surface feature small-sized roughness. The frequency of autovibrations can reach 5000 Hz and more.

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