2026-09-22T08:37:19Zhttps://api.repository.cam.ac.uk/server/oai/request

oai:www.repository.cam.ac.uk:1810/2876372021-04-21T19:16:30Zcom_1810_213729com_1810_256065col_1810_219485

An Investigation into Nonlinear Random Vibrations based on Wiener Series Theory 10.17863/CAM.34950 Demetriou, Demetris Langley, Robin 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 is made to relate the principles governing the successful spring model presented to the original nonlinear system. An iterative procedure is used to demonstrate the application of this method, which also enables this new modelling approach to be related to the SPF method. University of Cambridge 2019-07-20 Thesis Doctoral Doctor of Philosophy (PhD) en EPSRC and ΙΚΥΚ (Cypriot body) https://www.repository.cam.ac.uk/handle/1810/287637 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/fdf598da-d21f-4783-803a-790728d066fb/download ce147fb95f4762c8739bd5fd18f5e223 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/cb251b3a-8a55-416d-8cc0-bd119d01c997/download 87eda9de84448d1f82354d60eee3eb5f https://www.rioxx.net/licenses/all-rights-reserved/ 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