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research-article

Vibration Analysis in the Presence of Uncertainties Using Universal Grey System Theory

[+] Author and Article Information
Xintian Liu

University of Miami Department of Mechanical and Aerospace Engineering, University of Miami, CoralGables, FL 33146
xintianster@gmail.com

Singiresu S. Rao

University of Miami Department of Mechanical and Aerospace Engineering, University of Miami, Coral Gables, FL 33146
srao@miami.edu

1Corresponding author.

ASME doi:10.1115/1.4038940 History: Received March 04, 2017; Revised September 26, 2017

Abstract

The uncertainty present in many vibrating systems has been modeled using probabilistic, fuzzy or interval approaches depending on the nature of uncertainty present in the system. If the probability distributions of the uncertain parameters are known, the probabilistic approaches can be used. When the system parameters are vague and imprecise, the fuzzy methods are useful. In most practical vibration problems, the parameters of the system such as stiffness, damping and mass, initial conditions and/or external forces acting on the system are specified or known in the form of intervals or ranges. For such cases, the use of interval analysis appears to be most appropriate for predicting the ranges of the response quantities such as natural frequencies, free vibration response and forced vibration response under specified external forces. However, the accuracy of the results given by the interval analysis suffers from the so-called dependency problem which causes an undesirable expansion of the intervals of the computed results, which in some cases, can make the results unacceptable for practical implementation. This work presents a new methodology, called universal grey system (or number) theory, for the first time, for the analysis of vibrating systems whose parameters are described in terms of intervals or ranges. The computational feasibility and accuracy of the methodology are demonstrated by considering one and two degree-of-freedom systems. The proposed technique can be extended for the uncertainty analysis of any multi-degree of freedom system without much difficulty.

Copyright (c) 2017 by ASME
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