A Model Elucidating Significance of Cross-Correlations in Random Vibration Analysis

Author Type

Outside Researcher

Co-Author Type 1

Outside Researcher

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Studies in Applied Mechanics

Publication Status

Version of Record

Abstract

A simple two-degrees-of-freedom model is suggested for illustrating the significance of cross-correlations in random-vibration analysis. The system is composed of a single mass constrained by two springs in orthogonal directions, and appropriate dashpots, so that the mass can vibrate in a plane. The maximum mean-square displacement of the mass in the plane is investigated. An interesting analogy is established between the mean-square displacement and the transformation formula for the stress in a plane-stress state. It is also demonstrated that when the spring constants are equal and consequently the natural frequencies of undamped vibrations coalesce, omission of the cross-correlation terms entails an error of fifty percent in the maximum mean-square displacement, for perfectly positively correlated forces. For perfectly negatively correlated forces, the error is unbounded. © 1986 Elsevier B.V.

First Page

101

Last Page

112

DOI

10.1016/B978-0-444-42665-9.50013-X

Publication Date

1-1-1986

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