The response spectral density of a nonlinear system under broad band random excitation : A numerical simulation approach

Thaniotis, Elias Michael A (1982) The response spectral density of a nonlinear system under broad band random excitation : A numerical simulation approach. PhD thesis, University of Glasgow.

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The object of this study is to obtain the response spectra of the Duffing system excited by a Gaussian broad band random process, through the use of numerical simulations and to identify behavioural patterns of these spectra. The task was greatly simplified by the use of dimensional analysis. In Chapter 4 this method is applied to the Duffing system. The products of this non-dimensionalisation of the system under Gaussian broad band random excitation are the non dimensional quantities k2 Sx-(o)/S1, betaSx-(o)√(k/m), betaS,/√mk3, betasigma2x, c/2√km (the first three were symbolized by the capital Greek letters A,B, Gamma and zeta for c/2 km) where S, is the excitation spectrum intensity, Sx-(o) the displacement response spectrum and sigma2x the response displacement variance. Of these quantities only two are sufficient to describe the system completely under the aforementioned excitation namely Gamma and zeta. Simple examination of the above quantities revealed the possibility of direct relation of the quantities Gamma/zeta and betasigma2x. A parabolic relation was proved using the equivalent linearization technique and was verified by the findings of the simulation technique and the probabilistic information derived through the solution of the appropriate Fokker-Planck equation. Further it was found that the response spectra of the Duffing system under broad band excitation could be described with reasonable accuracy as functions of one variable, the ratio Gamma/zeta. Finally the applicability of the above findings and of the equivalent linearization technique for the Duffing system under band limited and high pass filtered random processes was investigated. It is worth noting that the findings of this study apply equally to 'large' and 'small' nonlinearities and it is hoped that it will provide a better understanding of these terms as applied in different approaches to this problem.

Item Type: Thesis (PhD)
Qualification Level: Doctoral
Additional Information: Adviser: J D Robson
Keywords: Mechanical engineering
Date of Award: 1982
Depositing User: Enlighten Team
Unique ID: glathesis:1982-72024
Copyright: Copyright of this thesis is held by the author.
Date Deposited: 17 May 2019 13:20
Last Modified: 17 May 2019 13:20

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