Numerical computation of nonlinear normal modes using HBM and ANM

Abstract

These notes correspond to the four lectures given by Bruno Cochelin at the CISM course on “Modal Analysis of Nonlinear Mechanical Systems” held at Udine, from 25 to 29 june 2012. The goal is to describe numerical methods which are complementary to those presented in the previous chapter by Gaetan Kerschen. Once again a conservative nonlinear normal mode will be seen as a one-parameter familly of periodic orbits. The Harmonic Balance Method (HBM) will be used for computing periodic solutions and the Asymptotic Numerical Method (ANM) will be used for the continuation of these periodic solutions. The methods and the results presented above have been obtained with the collaboration of S. Bellizzi, S. Karkar, E.H. Moussi and C. Vergez.