Nonlinear normal modes in mechanical systems: concept and computation with numerical continuation

Silva Bernárdez, Alejandro (2016). Nonlinear normal modes in mechanical systems: concept and computation with numerical continuation. Proyecto Fin de Carrera / Trabajo Fin de Grado, E.T.S.I. Industriales (UPM).

Description

Title: Nonlinear normal modes in mechanical systems: concept and computation with numerical continuation
Author/s:
  • Silva Bernárdez, Alejandro
Contributor/s:
  • Zarzo Altarejos, Alejandro
Item Type: Final Project
Date: 13 April 2016
Subjects:
Freetext Keywords: nonlinear normal modes, mechanical systems, vibration theory, modal analysis, nonlinear dynamics, harmonic balance, numerical continuation, matlab, NNMcont
Faculty: E.T.S.I. Industriales (UPM)
Department: Matemática Aplicada a la Ingeniería Industrial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

The purpose of this Project is, first and foremost, to disclose the topic of nonlinear vibrations and oscillations in mechanical systems and, namely, nonlinear normal modes NNMs to a greater audience of researchers and technicians. To do so, first of all, the dynamical behavior and properties of nonlinear mechanical systems is outlined from the analysis of a pair of exemplary models with the harmonic balanced method. The conclusions drawn are contrasted with the Linear Vibration Theory. Then, it is argued how the nonlinear normal modes could, in spite of their limitations, predict the frequency response of a mechanical system. After discussing those introductory concepts, I present a Matlab package called 'NNMcont' developed by a group of researchers from the University of Liege. This package allows the analysis of nonlinear normal modes of vibration in a range of mechanical systems as extensions of the linear modes. This package relies on numerical methods and a 'continuation algorithm' for the computation of the nonlinear normal modes of a conservative mechanical system. In order to prove its functionality, a two degrees of freedom mechanical system with elastic nonlinearities is analized. This model comprises a mass suspended on a foundation by means of a spring-viscous damper mechanism -analogous to a very simplified model of most suspended structures and machines- that has attached a mass damper as a passive vibration control system. The results of the computation are displayed on frequency energy plots showing the NNMs branches along with modal curves and time-series plots for each normal mode. Finally, a critical analysis of the results obtained is carried out with an eye on devising what they can tell the researcher about the dynamical properties of the system.

More information

Item ID: 40360
DC Identifier: http://oa.upm.es/40360/
OAI Identifier: oai:oa.upm.es:40360
Deposited by: Biblioteca ETSI Industriales
Deposited on: 03 Jun 2016 10:36
Last Modified: 03 Jun 2016 10:36
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