Approximate Solution of High-Frequency-Factor Vibrations of Rigid Bodies on Elastic Media

1971 ◽  
Vol 38 (1) ◽  
pp. 111-117 ◽  
Author(s):  
A. O. Awojobi

The mixed boundary-value problems of the vibrations of rigid bodies on elastic media are generally considered in the low-frequency-factor range. It is first established that, quite apart from a consideration of resonance, the usual assumption that this range predominates in practice is erroneous. The present work, therefore, is concerned with vibrations at frequency factors which are much greater than unity. Five cases have been considered: torsional vibration of a rigid circular body on a semi-infinite elastic medium and on an infinitely wide elastic stratum on a rigid bed; vertical vibration of a rigid circular body and of an infinitely long rectangular body on a semi-infinite elastic medium; rocking of a long rectangular body on a semi-infinite elastic medium. An estimate of both the unknown dynamic stress distribution under the rigid bodies and their amplitude responses has been obtained by finding an approximate solution to the exact governing dual integral equations. It is shown that at high-frequency factors, stress distributions are approximately constant for vertical vibrations and vary linearly from the center for rotational vibrations as in a Winkler model of theoretical soil statics contrary to increasing stresses with infinite edge stresses for low-frequency and static stress distributions of rigid bodies on elastic half space. We also obtain the important conclusion for amplitude response that it is predominantly governed by the inertia of the bodies because the contribution due to the dispersion of waves in the elastic medium is generally of a lower order of frequency factor than the inertia term except for an incompressible medium which has been analyzed separately and found to be of the same order leading to expressions for equivalent inertia of the vibrating medium. The theoretical results are used to derive the “tails” of resonance curves for both half space and stratum cases where experimental results are available. The agreement is fair and improves with increasing frequency factor.

1966 ◽  
Vol 33 (3) ◽  
pp. 547-552 ◽  
Author(s):  
A. O. Awojobi

Dual integral equations representing the mixed boundary-value problem of the rocking of an infinitely long, rigid rectangular body on the free surface of a semi-infinite elastic medium are here solved. Dynamic stress distributions under the rigid body and resonance curves for motion of the body are derived from the solution of these equations. A graphical representation of the theoretical results provides a novel method for estimating Poisson’s ratio of soil from a knowledge of the rocking frequency of a building. Suitable published results of tests on actual buildings have been used to indicate the application of this method.


This mixed boundary-value problem gives rise to a set of dual integral equations which have not hitherto been solved. Four cases are analysed: the vertical translation and rotation about an axis normal to the surface of a rigid circular body and the vertical translation and rocking of an infinitely long rigid rectangular body. The dynamic stress distributions under the rigid bodies are determined and are shown to reduce to the known static distributions for zero frequency factors. The dual integral equations are solved by a series of expansion procedures. The calculated response curves for translation and rotation of a rigid circular body are compared with the experimental results by Arnold, By croft & Warburton (1955) and are shown to be an improvement over other approximate theories. A suggestion is made for using the results of this analysis for the determination of the dynamic elastic properties of a soil in situ .


Author(s):  
G. Y. Fan ◽  
J. M. Cowley

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.


Author(s):  
M. T. Postek ◽  
A. E. Vladar

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.


1992 ◽  
Vol 1 (4) ◽  
pp. 52-55 ◽  
Author(s):  
Gail L. MacLean ◽  
Andrew Stuart ◽  
Robert Stenstrom

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.


1971 ◽  
Vol 36 (4) ◽  
pp. 527-537 ◽  
Author(s):  
Norman P. Erber

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.


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

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.


1998 ◽  
Vol 2 ◽  
pp. 115-122
Author(s):  
Donatas Švitra ◽  
Jolanta Janutėnienė

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.


2019 ◽  
Vol 85 (1(I)) ◽  
pp. 64-71 ◽  
Author(s):  
M. M. Gadenin

The cycle configuration at two-frequency loading regimes depends on the number of parameters including the absolute values of the frequencies and amplitudes of the low-frequency and high-frequency loads added during this mode, the ratio of their frequencies and amplitudes, as well as the phase shift between these harmonic components, the latter having a significant effect only with a small ratio of frequencies. Presence of such two-frequency regimes or service loading conditions for parts of machines and structures schematized by them can significantly reduce their endurance. Using the results of experimental studies of changes in the endurance of a two-frequency loading of specimens of cyclically stable, cyclically softened and cyclically hardened steels under rigid conditions we have shown that decrease in the endurance under the aforementioned conditions depends on the ratio of frequencies and amplitudes of operation low-frequency low-cycle and high-frequency vibration stresses, and, moreover, the higher the level of the ratios of amplitudes and frequencies of those stacked harmonic processes of loading the greater the effect. It is shown that estimation of such a decrease in the endurance compared to a single frequency loading equal in the total stress (strains) amplitudes can be carried out using an exponential expression coupling those endurances through a parameter (reduction factor) containing the ratio of frequencies and amplitudes of operation cyclic loads and characteristic of the material. The reduction is illustrated by a set of calculation-experimental curves on the corresponding diagrams for each of the considered types of materials and compared with the experimental data.


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