A variation of the intrinsic multiple-scale harmonic balance method
Author:
A. S. Atadan
Journal:
Quart. Appl. Math. 54 (1996), 401-406
MSC:
Primary 34C10; Secondary 34D20, 93C15
DOI:
https://doi.org/10.1090/qam/1402401
MathSciNet review:
MR1402401
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Abstract: A variation of the intrinsic multiple-scale harmonic balance method is introduced by combining the intrinsic multiple-scale harmonic balance method with the ideas introduced to modify the method of multiple-scales. The combined method has the advantage of having the desirable characteristics of both techniques. This is demonstrated by solving the Duffing equation.
A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, Wiley, New York, 1979
A. S. Atadan and K. Huseyin, A note on “A Uniformly Valid Asymptotic Solution for $\left ( {{d^2}y/d{t^2}} \right ) + \\ y = a + \varepsilon {y^2}$", J. Sound Vibr. 85, 129–131 (1982)
A. S. Atadan and K. Huseyin, An intrinsic method of harmonic analysis for non-linear oscillations (A perturbation technique), J. Sound Vibr. 95, 525–530 (1984)
K. Huseyin and R. Lin, An intrinsic multiple-scale harmonic balance method for non-linear vibration and bifurcation problems, Internat. J. Non-Linear Mech. 26, 727–740 (1991)
G. Veronis, A note on the method of multiple scales, Quart. Appl. Math. 38, 363–368 (1980)
A. H. Nayfeh, Perturbation Methods, Wiley, New York, 1973
K. Huseyin, Elastic Stability of Structures Under Combined Loading, Thesis, University College, London University, England, 1976
K. Huseyin, Nonlinear Theory of Elastic Stability, Noordhoff, Leiden, 1975
K. Huseyin, Multiple Parameter Stability Theory and its Applications. Bifurcations, Catastrophes, Instabilities, Oxford Engineering Science Series, vol. 18, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1986
A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, Wiley, New York, 1979
A. S. Atadan and K. Huseyin, A note on “A Uniformly Valid Asymptotic Solution for $\left ( {{d^2}y/d{t^2}} \right ) + \\ y = a + \varepsilon {y^2}$", J. Sound Vibr. 85, 129–131 (1982)
A. S. Atadan and K. Huseyin, An intrinsic method of harmonic analysis for non-linear oscillations (A perturbation technique), J. Sound Vibr. 95, 525–530 (1984)
K. Huseyin and R. Lin, An intrinsic multiple-scale harmonic balance method for non-linear vibration and bifurcation problems, Internat. J. Non-Linear Mech. 26, 727–740 (1991)
G. Veronis, A note on the method of multiple scales, Quart. Appl. Math. 38, 363–368 (1980)
A. H. Nayfeh, Perturbation Methods, Wiley, New York, 1973
K. Huseyin, Elastic Stability of Structures Under Combined Loading, Thesis, University College, London University, England, 1976
K. Huseyin, Nonlinear Theory of Elastic Stability, Noordhoff, Leiden, 1975
K. Huseyin, Multiple Parameter Stability Theory and its Applications. Bifurcations, Catastrophes, Instabilities, Oxford Engineering Science Series, vol. 18, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1986
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Article copyright:
© Copyright 1996
American Mathematical Society
