On the existence of periodic solutions and normal mode vibrations of nonlinear systems
Authors:
C. H. Cooke and R. A. Struble
Journal:
Quart. Appl. Math. 24 (1966), 177-193
MSC:
Primary 34.45
DOI:
https://doi.org/10.1090/qam/201732
MathSciNet review:
201732
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Additional Information
- R. M. Rosenberg and C. P. Atkinson, On the natural modes and their stability in nonlinear two-degree-of-freedom systems, J. Appl. Mech. 26 (1959), 377–385. MR 0108009
- R. M. Rosenberg, Normal modes of nonlinear dualmode systems, J. Appl. Mech. 27 (1960), 263–268. MR 0111194
- R. M. Rosenberg and C. S. Hsu, On the geometrization of normal vibrations of nonlinear systems having many degrees of freedom, Analytic methods in the theory of non-linear vibrations (Proc. Internat. Sympos. Non-linear Vibrations, Vol. I, 1961) Izdat. Akad. Nauk Ukrain. SSR, Kiev, 1963, pp. 380–416 (English, with Russian summary). MR 0159084
- R. M. Rosenberg, On normal mode vibrations, Proc. Cambridge Philos. Soc. 60 (1964), 595–611. MR 163464
- R. M. Rosenberg, On normal vibrations of a general class of nonlinear dual-mode systems, Trans. ASME Ser. E. J. Appl. Mech. 28 (1961), 275–283. MR 120796
- R. M. Rosenberg and J. K. Kuo, Nonsimilar normal mode vibrations of nonlinear systems having two degrees of freedom, Trans. ASME Ser. E. J. Appl. Mech. 31 (1964), 283–290. MR 188564
- R. M. Rosenberg, The normal modes of nonlinear $n$-degree-of-freedom systems, Trans. ASME Ser. E. J. Appl. Mech. 29 (1962), 7–14. MR 137340
W. Bogusz, Normal modes of nonlinear vibrations in two degrees of freedom systems, Nonlinear Vibration Problems, Second Conference on Nonlinear Vibrations, Warsaw 245–251 (1962)
W. Szemplinska, Normal modes of a nonlinear two-degree-of-freedom system and their properties, Nonlinear Vibration Problems, Second Conference on Nonlinear Vibrations, Warsaw 192–206 (1962)
R. M. Rosenberg, On linearity and nonlinearity, Nonlinear Vibration Problems, Second Conference on Nonlinear Vibrations, Warsaw 37–51 (1962)
R. M. Rosenberg and J. K. Kuo, On free vibrations of strongly nonlinear systems with many degrees of freedom, Nonlinear Vibration Problems, Second Conference on Nonlinear Vibrations, Warsaw 331–339 (1962)
- J. H. Heinbockel and R. A. Struble, Periodic solutions for differential systems with symmetries, J. Soc. Indust. Appl. Math. 13 (1965), 425–440. MR 181798
- Jack K. Hale, Oscillations in nonlinear systems, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1963. MR 0150402
- Raimond A. Struble, Nonlinear differential equations, International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1961. MR 0130408
R. M. Rosenberg and C. P. Atkinson, On the natural modes and their stability in nonlinear two-degree-of-freedom systems, J. of Appl. Mech. 26, 377–385 (1959)
R. M. Rosenberg, Normal modes of nonlinear dual-mode systems, J. of Appl. Mech. 27, 263–268 (1960)
R. M. Rosenberg 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)
R. M. Rosenberg, On the existence of normal mode vibrations of nonlinear systems with two degrees of freedom, Quarterly of Appl. Math. 22, 217–234 (1964)
R. M. Rosenberg, On normal vibrations of a general class of nonlinear dual-mode systems, J. of Appl. Mech. 28, 275–283 (1961)
R. M. Rosenberg and J. K. Kuo, Nonsimilar normal mode vibrations of nonlinear systems having two degrees of freedom, J. of Appl. Mech. 31, 283–290 (1964).
R. M. Rosenberg, The normal modes of nonlinear n-degree-of-freedom systems, J. of Appl. Mech. 29, 7–14 (1962)
W. Bogusz, Normal modes of nonlinear vibrations in two degrees of freedom systems, Nonlinear Vibration Problems, Second Conference on Nonlinear Vibrations, Warsaw 245–251 (1962)
W. Szemplinska, Normal modes of a nonlinear two-degree-of-freedom system and their properties, Nonlinear Vibration Problems, Second Conference on Nonlinear Vibrations, Warsaw 192–206 (1962)
R. M. Rosenberg, On linearity and nonlinearity, Nonlinear Vibration Problems, Second Conference on Nonlinear Vibrations, Warsaw 37–51 (1962)
R. M. Rosenberg and J. K. Kuo, On free vibrations of strongly nonlinear systems with many degrees of freedom, Nonlinear Vibration Problems, Second Conference on Nonlinear Vibrations, Warsaw 331–339 (1962)
J. H. Heinbockel and R. A. Struble, Periodic solutions for differential systems with symmetries, J. Soc. Indust. Appl. Math. 13, 425–440 (1965)
J. K. Hale, Oscillations in Nonlinear Systems, McGraw-Hill Book Co., New York (1963)
R. A. Struble, Nonlinear Differential Equations, McGraw-Hill Book Co., New York (1962)
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Article copyright:
© Copyright 1966
American Mathematical Society
