Probability of Response to Evolutionary Process

by Polihronis-Thomas Demetriou Spanos, (A.M.ASCE), Asst. Prof. of Civ. Engrg.; Univ. of Texas, Austin, Tex.,
Loren D. Lutes, (M.ASCE), Assoc. Prof. of Civ. Engrg.; Rice Univ., Houston, Tex.,

Serial Information: Journal of the Engineering Mechanics Division, 1980, Vol. 106, Issue 2, Pg. 213-224

Document Type: Journal Paper


The probability density function of the response amplitude of a lightly damped linear oscillator subjected to a broad-band nonstationary process with evolutionary spectrum is examined. By using a combination of deterministic and stochastic averaging a one-dimensional diffusion equation is obtained that approximately governs the time evolution of the probability density function of the response amplitude. Based on the diffusion equation it is proved that the nonstationary probability density of the response amplitude can be approximated by a Rayleigh distribution with a time dependent scaling variable. An equation for the analytical determination of the scaling variable is presented.

Subject Headings: Probability | Fouling | Damping | Oscillations | Stationary processes | Probability distribution | Time dependence | Linear analysis

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