The increasing demand for eco-sustainable structures and low-carbon emission systems is driving the research in many engineering fields, pushing the boundaries of scientific knowledge. High-performance structures, i.e. more efficient and lighter structures, are required to comply with the continuously more stringent regulations, nowadays imposed by many countries. This undermines the linear approximation used for modelling the behaviour of mechanical systems and structures, exposing their ultimately nonlinear nature. In this context, the need for a better understanding of the nonlinear dynamics behaviour of mechanical structures is becoming of primary importance, serving as a motivation for this work. In the literature, many authors have investigated the nonlinear behaviour of mechanical systems, mostly focusing on simplified mathematical representation with a single degree of freedom, especially in the analysis that involves the study of the global dynamic behaviour of the systems. This is particularly evident for systems which show strong nonlinear behaviour, e.g. systems with contact and impact, whose dynamics are extremely complicated and rich. In addition, it is not well known how accurate the identified mathematical models are, especially under which conditions they fail to capture the system dynamics from a qualitative and quantitative point of view. This thesis focuses on the dynamics of multi-degree freedom systems that exhibit strong nonlinear behaviours and aims to improve the tools/methods for their analysis and identification. In particular, mechanical systems with two degrees of freedom and piecewise (non-smooth) stiffness characteristics are considered. The dynamics of the systems are studied from a numerical and experimental point of view, tackling practical problems that currently represent an issue for their analysis and identification. Firstly, the rich dynamics of the system are investigated using numerical procedures. The presence of multiple period-doubling isolas and a bifurcation of the backbone curve is numerically proven using path-following techniques and numerical integration schemes. This represents an improvement in the fundamental understanding of the dynamics and bifurcation mechanisms of two-degree-of-freedom piecewise systems. Then, the effect of smoothing functions in approximating piecewise stiffness characteristics is assessed via a comparison of the dynamics of the approximate and non-approximate systems. It is demonstrated that the usage of the smoothing function permits obtaining a high level of accuracy, especially when chaos or quasi-periodic behaviours are avoided, significantly reducing the computational effort of the numerical calculations and simplifying the overall procedure. To prove the existence of bifurcation of the backbone curves and the presence of period doubling isolas encountered during the numerical analyses, an experimental test rigs are designed and tested exciting the main structure in two different ways, i.e. using an asymmetric (test-rig #1) and symmetric excitation (test-rig #2) condition. The obtained results confirm the existence of the investigated nonlinear phenomena and provide an accurate base of experimental data that can be used for testing nonlinear models and/or methods for parameters identification. Building on existing techniques, a novel method for the identification of nonlinear systems is proposed. The method, named the Nonlinear Restoring Force (NRF) Method, is capable of interfacing with linear identification methods and can be easily implemented in current industrial identification procedures, improving the accuracy of the identified models. The proposed method is used to identify the parameters of reduced-order models associated with the experimental test rigs. The identified reduced-order models are then validated against experimental results, using levels of excitation that are different from the one used for the identification process. This demonstrates the efficacy of the proposed identification method and proves that the identified reduced-order models are capable to capture the dynamics of strongly nonlinear systems from a qualitative and quantitative point of view.
| Date of Award | 8 Oct 2024 |
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| Original language | English |
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| Awarding Institution | - University Of Strathclyde
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| Sponsors | University of Strathclyde |
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| Supervisor | Maurizio Collu (Supervisor) & Andrea Coraddu (Supervisor) |
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