Probability Distribution of Extremes of Von Mises Stress in Randomly Vibrating Structures

[+] Author and Article Information
Sayan Gupta

Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, Indiagupta.sayan@gmail.com

C. S. Manohar1

Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, Indiamanohar@civil.iisc.ernet.in


Corresponding author. Telephone: +91 80 2293 3121; Fax: +91 80 2360 0404.

J. Vib. Acoust 127(6), 547-555 (Feb 22, 2005) (9 pages) doi:10.1115/1.2110865 History: Received May 17, 2004; Revised February 22, 2005

The problem of determining the probability distribution function of extremes of Von Mises stress, over a specified duration, in linear vibrating structures subjected to stationary, Gaussian random excitations, is considered. In the steady state, the Von Mises stress is a stationary, non-Gaussian random process. The number of times the process crosses a specified threshold in a given duration, is modeled as a Poisson random variable. The determination of the parameter of this model, in turn, requires the knowledge of the joint probability density function of the Von Mises stress and its time derivative. Alternative models for this joint probability density function, based on the translation process model, combined Laguerre-Hermite polynomial expansion and the maximum entropy model are considered. In implementing the maximum entropy method, the unknown parameters of the model are derived by solving a set of linear algebraic equations, in terms of the marginal and joint moments of the process and its time derivative. This method is shown to be capable of taking into account non-Gaussian features of the Von Mises stress depicted via higher order expectations. For the purpose of illustration, the extremes of the Von Mises stress in a pipe support structure under random earthquake loads, are examined. The results based on maximum entropy model are shown to compare well with Monte Carlo simulation results.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 1

Schematic diagram of the support for the fire-water system in a nuclear power plant; all dimensions are in mm

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Figure 2

Power spectral density functions for the stress components at the root of the cantilever; Sii denotes the psd of the stress component σii, (i=1,2,4)

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Figure 3

Probability distribution function for V(t)

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Figure 4

Probability distribution function for V̇(t)

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Figure 5

Exceedance probability of Von Mises stress




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