Effects of weak non-linearities on modal analysis

A. F. Vakakis, D. J. Ewins

Research output: Contribution to journalArticlepeer-review


In this work the distortions in the receptance plots of forced non-linear mechanical systems are examined. Weak non-linearities of stiffness and damping are considered, and approximate harmonic steady-state responses are evaluated using the method of equivalent linearisation. It is found that in the case of pure damping non-linearities, the frequency of maximum frequency separation in the receptance Nyquist plot is approximately equal to the natural frequency of the corresponding linearised system. However, when stiffness non-linearities are encountered, the maximum frequency separation is influenced by two non-linear terms: one accounting for the dependence of the equivalent natural frequency on the stiffness non-linearity, and the other accounting for the asymmetry of the Bode diagram. Based on the results of the analysis presented in this paper, a method for identifying and quantifying weak non-linearities in the frequency responses of practical systems is suggested. The applicability of the proposed technique is then tested with theoretical and experimental data.

Original languageEnglish (US)
Pages (from-to)175-198
Number of pages24
JournalMechanical Systems and Signal Processing
Issue number2
StatePublished - Mar 1994

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Signal Processing
  • Civil and Structural Engineering
  • Aerospace Engineering
  • Mechanical Engineering
  • Computer Science Applications


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