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

Demetrios G. Magiros
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Demetrios G. Magiros: New York University

Chapter 16 in Selected Papers of Demetrios G. Magiros, 1985, pp 220-249 from Springer

Abstract: 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.

Keywords: Nonlinear System; Singular Point; Saddle Point; Integral Curf; Harmonic Solution (search for similar items in EconPapers)
Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-5368-0_16

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DOI: 10.1007/978-94-009-5368-0_16

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