Periodic solutions of high accuracy to the forced Duffing equation: Perturbation series in the forcing amplitude
- 1 July 1987
- journal article
- research article
- Published by Cambridge University Press (CUP) in The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- Vol. 29 (1) , 21-38
- https://doi.org/10.1017/s0334270000005609
Abstract
“Steady state” periodic solutions are sought to the forced Duffing equation. The solutions are expressed as formal Fourier series, giving rise to an infinite system of non-linear algebraic equations for the Fourier coefficients. This system is then solved using perturbation series in the amplitude of the forcing term. Solution profiles of high accuracy and phase-plane orbits are presented. The existence of limiting values of the forcing amplitude is discussed, and points of non-linear resonance are identified.Keywords
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