Random Vibration in Mechanical Systems by Stephen H. Crandall, William D. Mark

By Stephen H. Crandall, William D. Mark

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Rice, Mathematical analysis of random noise, Bell System Tech. J. 23, 282-332 (1944); 24, 46-156 (1945). Reprinted in N . " Dover, New York, 1954. 2. H. M. James, N . B. Nichols, and R. S. Phillips, "Theory of Servomechanisms," McGraw-Hill, New York, 1947. 3. J. H. Laning and R. H. Battin. " McGraw-Hill, New York, 1956. 4. W. B. Davenport and W. L. " McGraw-Hill, New York, 1958. 5. J. S. " Wiley, New York, 1958. 6. D. " McGraw-Hill, New York, 1960. 7. S. H. " Technology Press and Wiley, New York, 1958.

Schematic diagram of measurement of spectral density G(œ0) of sample function/(i). function f(t) is filtered, squared, and averaged over a relatively long interval T. The measured quantity z(t) depends on the sample f(t) and also on the three parameters ω0, Δω and T of the measuring system. It can be shown [19] that when Δω is small and T is long, then z is an approximation to Δω G(œ0) where G(œ) is the indivi­ dual spectral density of f(t). Strictly speaking, the true spectral density G(w0) can only be obtained by a limiting process in which T-^oo and then Δω —* 0 (the order of the limiting processes here cannot be interchanged [18]).

73) depends on the normal or Gaussian assumption. In narrow-band but non- 53 REFERENCES normal processes these two distributions are generally different [27]. Again it should be noted that if the population of peaks were restricted to those occurring in a single sample function then the distribution of peak values would in general be different from Eq. 73) unless the process was ergodic. REFERENCES 1. S. O. Rice, Mathematical analysis of random noise, Bell System Tech. J. 23, 282-332 (1944); 24, 46-156 (1945).

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