Identification of structural non-linearities using describing functions and the Sherman-Morrison method

Ozer M. B., ÖZGÜVEN H. N., Royston T. J.

MECHANICAL SYSTEMS AND SIGNAL PROCESSING, vol.23, no.1, pp.30-44, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1016/j.ymssp.2007.11.014
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.30-44
  • Keywords: Non-linear structural dynamics, Non-linear identification, Non-linear structural identification, OF-FREEDOM SYSTEMS, HARMONIC RESPONSE
  • Middle East Technical University Affiliated: Yes


In this study, a new method for type and parametric identification of a non-linear element in an otherwise linear structure is introduced. This work is an extension of a previous study in which a method was developed to localize non-linearity in multi-degree of freedom systems and to identify type and parameters of the non-linear element when it is located at a ground connection of the system. The method uses a describing function approach for representing the non-linearity in the structure. The describing function contains only the first harmonic terms. The Sherman-Morrison matrix inversion method is used in the present study to put the response expression in a form where the non-linearity term can be isolated. Using measured responses one can calculate the value of the describing function representation of the non-linear element and thus perform the identification. This new method can be used for type and parametric identification of a non-linear element between any two coordinates of the system. Case studies are given to demonstrate the applicability of the method. (C) 2007 Elsevier Ltd. All rights reserved.