Stability analysis and non-linear behaviour of structural systems using the complex non-linear modal analysis (CNLMA)

Abstract

Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimation of the non-linear behavior of structural system, and it is applied to a complex system with quadratic and cubic non-linearities. Results from this non-linear method are compared with results obtained by integrating the full original non-linear system. This procedure appears very interesting in regard to computational time, formulation, and also necessitates very few computer resources. Thus the CNLMA is suited to computational implementation for various complex non-linear system with many degrees-of-freedom.