An Investigation into Nonlinear Random Vibrations based on Wiener Series Theory
type: CreativeWork
description: In support of society’s technological evolution, the study of nonlinear systems in engineering and sciences has become a vital research area. Aiming to contribute in this field, this thesis investigates the behaviour of nonlinear systems using the ‘Wiener theories’. As a useful example the Duffing oscillator is investigated in this work. In many real-life applications, nonlinear systems are excited randomly so this work examines systems under white-noise excitation using the Wiener series. Equivalent Linearisation (EL) is a well-known and simple method that approximates a nonlinear system by an equivalent linear system. However, it has deficiencies which this thesis attempts to improve. Initially, the performance of EL for different types of nonlinearities will be assessed and an alternative method to enhance it is suggested. This requires the calculation of the first Wiener kernel of various system defined quantities. The first Wiener kernel, as it will be shown, is the foundation of this research and a central element of the Wiener theory. In this thesis, an analytical proof to explain the interesting behaviour of the first Wiener kernel for a system with nonlinear stiffness is included using an energy transfer approach. Furthermore, the method mentioned above to enhance EL known as the Single-Pole Fit method (SPF) is to be tested for different kinds of systems to prove its robustness and validity. Its direct application to systems with nonlinear stiffness and nonlinear damping is shown as well as its ability to perform for systems with two degrees of freedom where an extension of the SPF method is required to achieve the desired solution. Finally, an investigation to understand and replicate the complex behaviour observed by the first Wiener kernel in the early chapters is carried out. The groundwork for this investigation is done by modelling an isolated nonlinear spring with a series of linear filters and certain nonlinear operations. Subsequently, an attempt i…
abstract: In support of society’s technological evolution, the study of nonlinear systems in engineering and sciences has become a vital research area. Aiming to contribute in this field, this thesis investigates the behaviour of nonlinear systems using the ‘Wiener theories’. As a useful example the Duffing oscillator is investigated in this work. In many real-life applications, nonlinear systems are excited randomly so this work examines systems under white-noise excitation using the Wiener series. Equivalent Linearisation (EL) is a well-known and simple method that approximates a nonlinear system by an equivalent linear system. However, it has deficiencies which this thesis attempts to improve. Initially, the performance of EL for different types of nonlinearities will be assessed and an alternative method to enhance it is suggested. This requires the calculation of the first Wiener kernel of various system defined quantities. The first Wiener kernel, as it will be shown, is the foundation of this research and a central element of the Wiener theory. In this thesis, an analytical proof to explain the interesting behaviour of the first Wiener kernel for a system with nonlinear stiffness is included using an energy transfer approach. Furthermore, the method mentioned above to enhance EL known as the Single-Pole Fit method (SPF) is to be tested for different kinds of systems to prove its robustness and validity. Its direct application to systems with nonlinear stiffness and nonlinear damping is shown as well as its ability to perform for systems with two degrees of freedom where an extension of the SPF method is required to achieve the desired solution. Finally, an investigation to understand and replicate the complex behaviour observed by the first Wiener kernel in the early chapters is carried out. The groundwork for this investigation is done by modelling an isolated nonlinear spring with a series of linear filters and certain nonlinear operations. Subsequently, an attempt i…
author: Demetriou, Demetris
language: en
keywords: Wiener, Volterra, Wiener series, Nonlinear, Random, Nonlinear Random Vibrations, Vibrations, Stochastic, Equivalent Linearisation, Duffing Oscillator, kernel, first Wiener kernel, single-pole function, Wiener theory, iteration method
license: https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/cb251b3a-8a55-416d-8cc0-bd119d01c997/download
license: https://www.rioxx.net/licenses/all-rights-reserved/
date published: 2019-07-20
date modified: 2026-07-22T22:24:06Z
provider: Cambridge University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: University of Cambridge

PropertyValue
property ID: DOI
value: 10.17863/CAM.34950