Analytical study of similar normal modes and their bifurcations in a class of strongly non-linear systems

T. K. Caughey, A. Vakakis, J. M. Sivo

Research output: Contribution to journalArticle


The concept of similar normal mode is used to study the free oscillations of a class of strongly non-linear, two degree of freedom undamped systems. By using the so-called balancing diagrams, the bifurcations of normal modes can be conveniently studied for different forms of stiffness non-linearities. Consequently, the stability of the resulting free motions is analytically examined and the theoretical results are checked by numerical integration of the equations of motion.

Original languageEnglish (US)
Pages (from-to)521-533
Number of pages13
JournalInternational Journal of Non-Linear Mechanics
Issue number5
StatePublished - 1990
Externally publishedYes


ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

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