Non-Linear Periodic and Quasi-Periodic Vibrations in Mechanical Systems - On the use of the Harmonic Balance Methods

Abstract

In this chapter, the general formulation and extensions of the harmonic balance method will be presented. The chapter is divided into four parts. Firstly we propose to present the general formulation and the basic concept of the harmonic balance method to find periodic oscillations of non-linear systems. Secondly a generalization of the method is exposed to treat quasi-periodic solutions. Thirdly, a condensation procedure that keeps only the non-linear degrees of freedom of the mechanical system is described. This technique may be of great interest to reduce the original non-linear system and to calculate the dynamical behaviour of non-linear systems with many degrees of freedom. The last part presents the classical continuation procedures that let us follow the evolution of a solution as a system parameter varies.