Abstract
In the previous paper, exact solutions of the autonomous Duffing equation were obtained in terms of the Fourier series making use of the so-called q-expansion of the elliptic functions. A characteristic parameter which plays a central role in calculating the Fourier coefficients, must be determined as a root of the modulus equation essentially by a trial method. As for some algorithms as well as approximation formulae proposed in the previous Saper, a few extensions of the discussions are presented here to improve the accuracy. A new trial algorithm and a revised approximation formula are proposed for a case of ultra low frequency (strongly nonlinear square wave and pulse train), and a new expression of the Fourier coefficient is also discussed, which is suitable in particular for the case of quasi-linear oscillation. Some salient features of the solution are illustrated for the case of a snap-through spring system in a full swing as well as in half swing modes.
