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- W2000740869 abstract "In his paper, the author determines the stability of periodic solutions of (1) the general forced Duffing equation without damping, x¨+x+εf(x)=εE cosωt, f(x) a polynomial, ε≪1; (2) the forced Duffing equation with damping, x¨+εrẋ+αx+εx3=εE cos(ωt+ψ), ε≪1; and (3) the general forced Van der Pol equation, x¨−εf(ẋ)+x=εE cos(ωt+ψ), f(ẋ) an odd polynomial, ε≪1, by seeking conditions necessary to insure periodic or almost-periodic solutions of the corresponding variational equation. The former are obtained rigorously by means of an existence proof and the latter formally by perturbation series. A vertical tangent theorem is derived which states that the locus of the points of contact of the vertical tangents to the response curves is a stability boundary, since it coincides, in the first approximation, with the locus of periodic solutions of the variational equation. These techniques are illustrated by considering the forced vibrations of a triode oscillator with a fifth-order tube characteristic, this being a particular case of (3), where we set f(ẋ)=ẋ−13ẋ3+λẋ5." @default.
- W2000740869 created "2016-06-24" @default.
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- W2000740869 date "1951-12-01" @default.
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- W2000740869 title "Studies in Nonlinear Vibration Theory" @default.
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- W2000740869 doi "https://doi.org/10.1063/1.1699885" @default.
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