Contributions to the investigation of the nonlinear dynamics of immersed slender structures: reduced-order model analysis and their advantages.

• Ano de defesa: 2022
• Autor(a) principal: Lopes, Guilherme Jorge Vernizzi
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Analytical techniques; Dinâmica das estruturas; Estruturas offshore; Interação fluido-estrutura; Método de Galerkin; Métodos assintóticos; Nonlinear dynamics; Parametric excitation; Reduced-order models; Vortex-induced vibrations
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/3/3144/tde-25112022-083551/

In any problem of structural engineering, there is the need of creation of a mathematical model to represent the desired physical phenomenon, followed by its solution. The latter step may be done in various ways, being it through analytical solutions, or by means of low/high-order hierarchical numerical methods. In what concerns the low-hierarchy models, herein called reduced-order models, the technique and tools applied to extract them from the original model are of great importance. Although there are plenty of works in the literature using reduced-order models to analyse different problems, few works are focused solely on addressing qualitative aspects of the generation process of such models and their advantages as complementary design tools for engineering practice. Those aspects are investigated in this thesis, using the offshore engineering scenario as background for the applied examples and problem motivation. The investigations are started within the problem of parametric excitation of straight and flexible rods immersed in water. Different reduced-order models are conceived, using different functions to represent the displacement field. Analyses are then carried out to investigate the effect of using more detailed projection functions over the quality of the obtained models and which base is able to produce a minimal model, which presents great advantages in terms of analytical investigations and computational effort needed for simulations. Some analytical solutions directly obtained from the continuous model are also developed, being such solutions a form of reduced model themselves in the sense that they are able to describe the continuous field by solving a small number of defined variables. For this case, a simple yet effective polynomial solution is also developed for design use. Giving sequence, the case of initially curved elastic and immersed cables under support excitation is also considered. Again, different reduced-order models are conceived and compared in order to address the advantage of each model and to obtain a minimal one. Finally, flexible rods under vortex-induced vibrations are also an object of study. With the use of different reduced-order models it is shown how they limit the range of analysis in terms of the external fluid velocity range in which they can be applied. It is also shown how they may filter the response, limiting the analysis of cases where multi-frequency responses are present. In order to further reduce the order of the models for this scenario, a methodology to obtain the nonlinear normal modes for this problem is also presented. This allows the maximum possible reduction in the number of degrees of freedom to be analysed, without compromising the quality of the results. In the collection of results, it is shown the importance of detailed analysis in the procedure to obtain reduced-order models, specially in what concerns the displacement fields adopted for the solution. It is also shown the advantages in analysis of being able to obtain a minimal model, together with approaches to turn such models into useful design tools.