Abstract
In the preceding chapters, we have learned how to predict the statistics of the structural response (displacements, stresses, etc…) from the statistics of the random excitation. Most of the time, if the structure is linear, the response statistics are available in the form of PSD functions. From them, it is straightforward to evaluate the RMS response, but this is rarely enough to assess the reliabilty of the system, which depends on the failure mode of the structure.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S.T. ARIARATNAM and H.N. PI, On the first-passage time for envelope crossing for a linear oscillator, Int. Journal of Control, Vol.18, No 1, pp.89–96, 1973.
D.E. CARTWRIGHT and M.S. LONGUET-HIGGINS, The statistical distribution of the maxima of a random function, Proc. Roy. Soc. Ser. A, 2,97, pp.212–232, 1956.
H. CRAMER and M.R. LEADBETTER, Stationary and Related Stochastic Processes, Wiley, 1967.
S.H.CRANDALL, Zero crossings, peaks, and other statistical measures of random responses, The Journal of the Acoustical Society of America, Vol.35, No 11, pp.1693–1699, November 1963.
S.H. CRANDALL, K.L. CHANDIRAMANI and R.G.COOK, Some first passage problems in random vibration, ASME Journal of Applied Mechanics, Vol.33, pp.532–538, September 1966.
S.H. CRANDALL, First crossing probabilities of the linear oscillator, Journal of Sound and Vibration 12 (3), pp. 285–299, 1970.
A.G. DAVENPORT, Note on the distribution of the largest value of a random function with application to gust loading, Proc. Inst. Civ. Eng., Vol 28, pp.187196, 1964.
W.B. DAVENPORT, Probability and Random Processes, McGraw-Hill, 1970.
S. KRENK, Nonstationary narrow-band response and first-passage probability, ASME Journal of Applied Mechanics, Vol. 46, pp. 919–92. 4, December 1979.
W.C. LENNOX and D.A. FRASER, On the first-passage distribution for the envelope of a nonstationary narrow-band stochastic process. ASME Journal of Applied Mechanics, Vol. 41, pp. 793–797, September 1979.
Y.K. LIN, Probabilistic Theory of Structural Dynamics, McGraw-Hill, 1967.
Y.K. LIN, First-excursion failure of randomly excited structures, AIAA Journal, Vo1.8, No 4, pp.720–725, 1970.
R.H. LYON, On the vibration statistics of a randomly excited hard-spring oscillator II, The Journal of the Acoustical Society of America, Vol. 33, No 10, pp. 1395–1403, October 1961.
D. MIDDLETON, An Introduction to Statistical Communication Theory, McGraw-Hill, 1960.
A. PREUMONT, On the peak factor of stationary Gaussian processes, Journal of Sound and Vibration 100 (1), pp. 15–34, 1985.
R.L. RACICOT and F. MOSES, A first-passage approximation in random vibration, ASME Journal of Applied Mechanics, pp. 143–147, March 1971.
S.O. RICE, Mathematical analysis of random noise, Bell System Technical Journal, 23, pp.282–332, 1944; 24, pp.46–156, 1945. Reprinted in Selected Papers on Noise and Stochastic Processes, N.WAX ed., Dover, 1954.
J.B. ROBERTS, First passage time for the envelope of a randomly excited linear oscillator, Journal of Sound and Vibration, 46 (1), pp. 1–14, 1976.
G.P. SOLOMOS and P-T.D. SPANOS, Solution of the Backward-Kolmogorov equation for nonstationary oscillation problem. ASME Journal of Applied Mechanics, Vo1. 49, pp. 923–925, December 1982.
R.L. STRATONOVICH, Topics in the Theory of Random Noise, Vol. 2, Gordon and Breach, N-Y, 1967.
A.A. SVESHNIKOV, Applied Methods of the Theory of Random Functions, Pergamon Press, 1966.
E.H. VANMARCKE, Properties of spectral moments with applications to random vibration, ASCE Journal of Engineering Mechanics Division, EM2, PP-05- W, April 1972.
E.H. VANMARCKE, On the distribution of the first-passage time for normal stationary random processes, ASME Journal of Applied Mechanics, Vol.42, pp.215220, March 1975.
J.N. YANG and M. SHINOZUKA, On the first excursion probability in stationary narrow-band random vibration, ASME Journal of Applied Mechanics, Vol. 38, pp. 1017–1022, December 1971.
J.N. YANG and M. SHINOZUKA, On the first excursion probability in stationary narrow-band random vibration, II, ASME Journal of Applied Mechanics, Vol. 39, pp. 733–738, September 1972.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Preumont, A. (1994). Threshold Crossings, Maxima, Envelope and Peak Factor. In: Random Vibration and Spectral Analysis. Solid Mechanics and Its Applications, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2840-9_10
Download citation
DOI: https://doi.org/10.1007/978-94-017-2840-9_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4449-5
Online ISBN: 978-94-017-2840-9
eBook Packages: Springer Book Archive