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Subharmonics of Any Order in Nonlinear Systems of One Degree of Freedom: Application to Subharmonics of Order 1/3

In: Selected Papers of Demetrios G. Magiros

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  • Demetrios G. Magiros

    (New York University)

Abstract

This paper consists of two parts. In the first one we discuss the subharmonics of any order in the case where the nonlinearity enters in the elastic forces. The basic differential equation is with coefficients not necessarily small. The “steady state” and “transient” solutions of the differential equation, and the conditions for the existence of the subharmonics and their stability in a steady state are examined. In the second part of the paper an application is given, namely, the investigation of the subharmonics of order 1/3 according to the theory of the first part. An illustrated example is given, the “inverse problem” is examined, and the conditions for the stability and instability of the “harmonic solution” are found.

Suggested Citation

  • Demetrios G. Magiros, 1985. "Subharmonics of Any Order in Nonlinear Systems of One Degree of Freedom: Application to Subharmonics of Order 1/3," Springer Books, in: S. G. Tzafestas (ed.), Selected Papers of Demetrios G. Magiros, chapter 16, pages 220-249, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-5368-0_16
    DOI: 10.1007/978-94-009-5368-0_16
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