By Christi Lalanne

ISBN-10: 1417526335

ISBN-13: 9781417526338

ISBN-10: 1903996058

ISBN-13: 9781903996058

The majority of vibrations encountered within the genuine setting are random. by way of their very nature, such vibrations are complex. This quantity describes the permitting approach for simplification of the research required and the research of the sign within the frequency area. strength spectrum density is outlined, with precautions had to be taken in its calculation defined including the approaches (windowing, overlapping) had to increase effects. yet another, complementary procedure, the research of statistical homes of the time sign, is defined. this permits choice of the distribution legislation of the maxima of a random gaussian sign to be made up our minds and simplification of calculation of fatigue harm to be made via the avoidance of the direct counting of peaks.

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**Example text**

2] One could envisage the comparison of two random vibrations (assumed to be ergodic) from their Fourier spectra calculated using samples of duration T. This work is difficult, for it supposes the comparison of four curves two by two, each transform being made up of a real part and an imaginary part (or amplitude and phase). One could however limit oneself to a comparison of the amplitudes of the transforms, by neglecting the phases. We will see in the following paragraphs that, for reasons related to the randomness of the signal and the miscalculation which results from it, it is preferable to proceed with an average of the modules of Fourier transforms calculated for several signal samples (more exactly, an average of the squares of the amplitudes).

2), - calculating the rms value L^g of the signal collected at the output of each filter. The curve which would give Lrms with respect to f would be indeed a description of the spectrum of signal t(t), but the result would be different depending on the width Af derived from the filters chosen for the analysis. So, for a stationary noise, one filters the supposed broad band signal using a rectangular filter of filter width Af, centered around a central frequency f c , the obtained response having the aspect of a stable, permanent signal.

1. Fourier transform The Fourier transform of a non-periodic ^(t) signal, having a finite total energy, is given by the relationship: (t) e-lQt dt L(Q) = [2-1] -00 This expression is complex; it is therefore necessary in order to represent it graphically to plot: - either the real and the imaginary part versus the angular frequency Q, - or the amplitude and the phase, versus Q. Very often, one limits oneself to amplitude data. The curve thus obtained is called the Fourier spectrum [BEN 58]. 34 Random vibration The random signals are not of finite energy.

### Mechanical Vibrations and Shocks: Random Vibrations v. 3 (Mechanical vibration & shock) by Christi Lalanne

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