Probability of Response to Evolutionary Process

Polichronis-Thomas D. Spanos · Loren D. Lutes

57 citations0/0 files storedJournal of the Engineering Mechanics Division

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Probabilistic and Robust Engineering Design Vibration and Dynamic Analysis stochastic dynamics and bifurcation

Abstract

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.

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