Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the existence of normal mode of vibrations of nonlinear systems with two degrees of freedom

Author: R. M. Rosenberg
Journal: Quart. Appl. Math. 22 (1964), 217-234
DOI: https://doi.org/10.1090/qam/99954
MathSciNet review: QAM99954
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Abstract | References | Additional Information

Abstract: A nonlinear, conservative system having two degrees of freedom is considered. The potential energy is subject to certain restrictions which are consistent with the strain energy of springs. Then, the notion of transversals; i.e., of curves orthogonal to equipotential lines, is introduced in order to prove the existence of an in-phase and of an out-of-phase normal mode of vibration, no matter how nonlinear the springs. It is shown, that the transversals are also very helpful in the discussion of general motions of the system.

References [Enhancements On Off] (What's this?)

  • [1] R. M. Rosenberg, Normal modes of nonlinear dual-mode systems, J. Appl. Mech. 27 (1960) 263 MR 0111194
  • [2] R. M. Rosenberg, On normal vibrations of a general class of nonlinear dual-mode systems, J. Appl. Mech. 28 (1961) 275 MR 0120796
  • [3] R. M. Rosenberg, R. M. and C. S. Hsu, On the geometrization of normal vibrations of nonlinear systems having many degrees of freedom, Proceedings, IUTAM Symposium on Nonlinear Vibrations Kiev, 1963 MR 0159084
  • [4] R. M. Rosenberg, The normal modes of nonlinear n-degree-of-freedom systems, J. Appl. Mech. 29 (1962) 7 MR 0137340
  • [5] R. M. Rosenberg, and J. K. Kuo, Non-similar normal mode vibrations of nonlinear systems having two degrees of freedom, to be published in J. Appl. Mech.
  • [6] See for instance N. Minorski, Nonlinear oscillations, D. Van Nostrand Company, Inc. 1962, pp. 9-26
  • [7] H. Kauderer, Nichtlineare Mechanik, Springer Verlag, 1959, p. 599 MR 0145709

Additional Information

DOI: https://doi.org/10.1090/qam/99954
Article copyright: © Copyright 1964 American Mathematical Society

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