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On a Problem of Nonlinear Mechanics

In: Selected Papers of Demetrios G. Magiros

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  • Demetrios G. Magiros

    (Republic Aviation Corporation)

Abstract

The behavior of a forced oscillatory system which is linearly damped but nonlinear in the restoring force is investigated according to the author’s previous papers (Magiros, 1957, 1958). It is shown under which conditions the system may contain subharmonics of order 1/2. The amplitudes of the subharmonics and their components, and the bounds for the amplitude of the external force, are given in terms of the coefficients of the differential equation of the system, which are not necessarily very small, as well as the regions in the (c 1/c 3, I)-plane, where we have subharmonics with two, one, or neither amplitudes. Also discussed are the stability of the subharmonics, the free vibrations of the system, and the case when one of the coefficients of the nonlinear terms is zero.

Suggested Citation

  • Demetrios G. Magiros, 1985. "On a Problem of Nonlinear Mechanics," Springer Books, in: S. G. Tzafestas (ed.), Selected Papers of Demetrios G. Magiros, chapter 17, pages 250-262, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-5368-0_17
    DOI: 10.1007/978-94-009-5368-0_17
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