THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

References 615If the vibration measurements are sufficiently representative and the process isstationary, the root-mean-square value is then given by( ∫ 1 T) ∫ ∞xrms 2 = lim x 2 (t) dt = W ( f ) df = R(0)T →∞ T 00wherex 2 rms= root-mean-square value, g2R(0) = the autocorrelation function for τ = 0White NoiseWhite noise is a random signal which has a constant root-mean-square spectraldensity for all frequencies from zero to infinity, i.e.,W white ( f ) = W 0for 0 < f < ∞This idealization cannot be achieved physically, since it would amount to requiringan infinite amount of power. More realistically, band-limited white noise can beachieved and it is a random signal having a constant spectral density over a specifiedrange:W white ( f ) = W 0 f 1 < f < f 2White noise generators are produced to generate signals with random vibrationin amplitude and frequency, with relatively constant spectral density over variousfrequency ranges.ReferencesBeranek, Leo L. (ed.). 1971. Noise and Vibration Control. New York: McGraw-Hill.Broch, J. T. June 1973. Mechanical and Shock Measurements. Nærum, Denmark: Brüel &Kjær Instruments Company.Brooks, P. 1986. Solving vibration problems on a PC. Sound and Vibration 20(11):26–32.Crandall, S. H. and Mark, W. D. 1963. Random Vibration in Mechanical Systems.New York: Academic Press.Crede, C. E. 1965. Shock and Vibration Concepts in Engineering Design. EnglewoodCliffs, NJ: Prentice Hall.Grandin, H. 1986. Fundamentals of the Finite Element Method. New York: Macmillan.Harris, Cyril M. (ed.). 1991. Handbook of Acoustical Measurements and Noise Control,3rd ed. New York: McGraw-Hill, Chapters 6–10.Harris, C. M. (ed.). 1988. Shock and Vibration Handbook, 3rd ed. New York: McGraw-Hill.Huebner, K. H. and Thornton, E. A. 1982. The Finite Element Method for Engineers, 2nded. New York: Wiley-Interscience.Hughes, T. J. R. 1987. The Finite Element Method—Linear Static and Dynamic FiniteElement Analysis. Englewood Cliffs, NJ: Prentice Hall.