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The geometry of random vibrations and solutions by FORM and SORM

Authors
Journal
Probabilistic Engineering Mechanics
0266-8920
Publisher
Elsevier
Publication Date
Volume
15
Issue
1
Identifiers
DOI: 10.1016/s0266-8920(99)00011-9
Keywords
  • Discretization
  • First-Order Reliability Method (Form)
  • Geometry
  • Non-Gaussian Processes
  • Out-Crossing Rate
  • Random Vibrations
  • Reliability
  • Second-Order Reliability Method (Sorm)
Disciplines
  • Mathematics

Abstract

Abstract The geometry of random vibration problems in the space of standard normal random variables obtained from discretization of the input process is investigated. For linear systems subjected to Gaussian excitation, the problems of interest are characterized by simple geometric forms, such as vectors, planes, half spaces, wedges and ellipsoids. For non-Gaussian responses, the problems of interest are generally characterized by non-linear geometric forms. Approximate solutions for such problems are obtained by use of the first- and second-order reliability methods (FORM and SORM). This article offers a new outlook to random vibration problems and an approximate method for their solution. Examples involving response to non-Gaussian excitation and out-crossing of a vector process from a non-linear domain are used to demonstrate the approach.

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