Tese: Stability analysis applied to mechanical, electromagnetic and electromechanical systems with parametric excitation
Aluno(a) : Natasha Barros de Oliveira HirschfeldtOrientador(a): Roberta Lima e Rubens Sampaio
Área de Concentração: Mecânica Aplicada
Data: 24/11/2022
Link para tese/dissertação: https://doi.org/10.17771/PUCRio.acad.61701
Resumo: Parametric excitation is a type of excitation that arises from time-varying coefficients in a system’s dynamics. More specifically, this dissertation deals with time-periodic coefficients. This type of excitation has been an extended topic of research from the fields of mechanics and electronics to fluid dynamics. It appears in problems involving dynamical systems, for example, as a way of controlling vibrations in self-excited systems, making this subject worthy of more investigations. By approaching stability in the sense of Lyapunov, this dissertation provides a didactic stability background from basic concepts, such as equilibrium points and phase diagrams, to more advanced ones, like parametric excitation and Floquet theory. The objects of study here are linear systems with time-periodic parameters. Floquet theory is used to make stability statements about the system’s trivial solutions. Several examples are discussed by making use of a developed numerical procedure to construct stability maps and phase diagrams. The examples presented herein encompass mechanical, electromagnetic and electromechanical systems. By making use of stability maps, several features that can be discussed in stability analysis are approached. Two different strategies to evaluate the stability of trivial solutions are compared: Floquet multipliers and the maximum value of Lyapunov characteristic exponents.