Efeitos do atraso sobre a estabilidade de sistemas mecânicos não lineares

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Universidade Federal de Goiás


Vibrations of mechanical systems have a wide field of research, where many work have been dedicated. Such importance is due to the fact that most human activities involve vibrations. It is worth noting that many device can suffer or produce vibrations, such as, machines, structures, motors, turbines. Vibratory systems, generally can produce complex behavior, thus the analysis of such dynamics behavior needs to use sophisticated mathematical tools. The mathematical model assigns important features of real processes with respect to linear and non-linear differential equations. In this work we are interested in the analysis of behavior of delayed mechanical systems. Time delayed can compromise the performance of controls even adding instability in the systems. On the other hand, write choose of delays can improve its performance. Systems with time delay, similar to ordinary systems, are molded by ordinary and/or partial differential equations, but, unlikely ordinary differential equations, delayed differential equations, also known as functional differential equations, are molded on Banach spaces with infinite dimension, which introduce serious difficulty in analysis of stability, since that, the spectra of solution semi-group associated with the linear part of the model can presents infinite eigenvalues. Thus, our contribution of the study of dynamics behavior of such systems will be in two directions. In the first one, we apply the perturbation method of multiple scales in themodel of differential equations, since that the system shows nonlinear vibrations. It is worth noting that the differential analysis used in the stage regarding differential equations in Banach spaces, which has infinite dimension, this approach differ substantially from standards approaches. Then we obtain numerical solutions for the amplitude at steady state using the Newton Raphson method and then we made a numerical analysis of the model of stability with delay and without delay to different parameters, using the Runge-Kuttamethod.



Vibrações mecânicas, Equações diferenciais com tempo de atraso, Modelagem matemática, Sistema de controle, Método de perturbação das múltiplas escalas, Métodos numéricos, Mechanical vibration, Differential equations with time delay, Mathematical modeling, Control system, Perturbation method of multiple scales, Numerical methods


FERREIRA, R. G. Efeitos do atraso sobre a estabilidade de sistemas mecânicos não lineares. 2016. 101 f. Dissertação (Mestrado em Modelagem e Otimização) - Universidade Federal de Goiás, Catalão, 2016.