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Shock and Vibration
Volume 7 (2000), Issue 4, Pages 217-227

Variable Modal Parameter Identification for Non-Linear Mdof Systems. Part I: Formulation and Numerical Validation

Y.H. Chong and M. Imregun

Imperial College of Science Technology and Medicine, Mechanical Engineering Department, Exhibition Road, London SW7 2BX, UK

Received 6 June 1999; Revised 5 January 2000

Copyright © 2000 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 superposition is combined with the normal non-linear mode technique, an approach that allows the formulation of a system identification procedure in terms of variable modal parameters. The numerical study was focused on a 4-DOF system with cubic stiffness non-linearity, and the modal parameters were obtained 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 linear model may be approximate. Similarly, the technique was found to be robust in the presence of measurement noise, though some adverse effects were observed for high noise levels. Once the variable modal parameters were extracted at some given force level, the non-linear responses were predicted at other force levels via synthesis of normal non-linear modes. The same responses were also obtained using a harmonic balance approach and very good agreement was obtained between the two sets of results. The procedure is well suited to the study of industrial cases because of its compatibility with existing finite element methods and linear modal analysis techniques.