Variable modal parameter identification for non-linear mdof systems. Part I: Formulation and numerical validation

This paper deals with the formulation of a frequency domain modal analysis technique that is applicable to weakly non-linear multi-degree of freedom ( MDOF) systems with well-separated modes. The concept of linear modal superp osition is combined with the normal non-linear mode technique, an approach that allows the formulation of a system identification procedure in terms o f variable modal parameters. The numerical study was focused on a 4-DOF sys tem with cubic stiffness non-linearity, and the modal parameters were obtai ned as functions of the modal amplitude. It was shown that the methodology was well suited to the study of practical cases for which the underlying li near model may be approximate. Similarly, the technique was found to be rob ust in the presence of measurement noise, though some adverse effects were observed for high noise levels. Once the variable modal parameters were ext racted at some given force level, the non-linear responses were predicted a t other force levels via synthesis of normal non-linear modes. The same res ponses were also obtained using a harmonic balance approach and very good a greement was obtained between the two sets of results. The procedure is wel l suited to the study of industrial cases because of its compatibility with existing finite element methods and linear modal analysis techniques.