Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Evaluation of Nonlinear Modes of a 2 DOF Oscillator using Poincaré Map
Submission Author:
Filipe Eduard Leite Ossege , DF
Co-Authors:
Filipe Eduard Leite Ossege, Aline Souza de Paula
Presenter: Filipe Eduard Leite Ossege
doi://10.26678/ABCM.COBEM2021.COB2021-0422
Abstract
The dynamics of nonlinear systems is crucial for the understanding of real life’s phenomena, since most of the dynamical systems given by nature are described by nonlinearities. Linear systems have normal modes that are orthogonal to each other. One way to define these modes is by synchronous time response of all degrees-of-freedom. In a similar way, nonlinear systems possess nonlinear modes. But, in contrast with linear systems, they are not normal and because of this they can be coupled. In such way, non excited frequencies can appear in the system‘s response, an unexpected behavior, due to nonlinear modes coupling. Understanding the nonlinear modes is a crucial role, as they described the system in a state that, with excitation, can lead to the breaking of the physical components of the machinery. Because of this, it is important to avoid the excitation of nonlinear modes, in order to prevent accidents in engineering projects and not to bear with avoidable costs. In this work, a nonlinear system with two degrees-of-freedom under free vibrations is studied using an numerical approach, based on the Poincaré map, that highlights the modes by singular points on a graph. The nonlinearity is provided by 3 nonlinear stiffness elements, represented by springs with cubic terms. The nonlinear modes for different values of stiffness and energy are obtained. The main objective of this paper is the identification of the nonlinear modes of this system by means of a numerical method, the Poincaré section, that does not require the extensive calculation of the analytic solution. The stability of the nonlinear modes is also analyzed. The obtained results are the identification of modes and how the variation of the system‘s parameters, such as energy, changes the quantity of modes and their stability. The main conclusion is that this technique can be used for the identification of nonlinear modes without the need of extensive calculations.
Keywords
nonlinear dynamics, nonlinear vibration, linear normal modes, nonlinear modes, Poincaré sections
