By P.O.A.L. Davies, M. Heckl, G.L. Koopmann, G. Bianchi

ISBN-10: 3211817107

ISBN-13: 9783211817100

ISBN-10: 3709128943

ISBN-13: 9783709128947

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1975 Longman spectral analysis. An Introduction to Random vibration and 2. S. G. 1966 John Wiley, New York Measurement and Analysis of Random Data 3. T. ments. 4. The Shock and Vibration Bulletin April 1966 US Naval Research Laboratory Washington, DC. Bulletin 35 Part 6. S. T. 1963 John Wiley and Sons Inc Engineering. Bruel and Kjaer Mechanical Vibration and Shock Measure- Shock and Vibration THEORY OF ACOUSTICS I Waves, Rays, and Statistical Fields The following two lectures on the theory of acoustics are intended to provide the scientist whose discipline is not primarily acoustics and vibration with a brief review of the terminology and methodology used throughout this advanced course.

The above properties are shown on the following graph of Rx versus separation timeT. T Figure 9 Illustrating properties of the autocorrelation function Rx(T) of a stationary random process x(t) As shown above, the auto correlation function describes certain properties of the non-deterministic random process as a function of the separation timeT. This function is deterministic and gives information about the frequency content of the random process indirectly. This is illustrated in figure 9 where the function R (T) reflects the frex quency content of the sample functions of a random process x(t).

Spectra 41 For a continuous frequency distribution from f =0 to f = 00 the mean square value of the random function is equal to the integral 00 I W(f ) df 0 (20) 0 0 which is identical to that given in equation (19). Thus as shown in figure 11, a plot of the mean square spectral density W(f) of a random function is a continuous curve and, at a frequency f , the power spectral density is represented by the average 0 height of a rectangle of unit width centered about the frequency f 0 • Figure 11 also shows a comparison of the spectrum of a wide and narrow band random signal.

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