抄録
Exact solutions of the autonomous Duffing equation including the so-called bistable spring system, are obtained in the Fourier expansion by using elliptic functions. The characteristic parameter J in the Fourier coefficients as well as the governing parameter m (or the complementary parameter m1) of the complete elliptic integral of the first kind, K(m), must be determined to satisfy conditions which arise due to the situation of the system and the non-dimensional natural frequency ν. In this paper three algorithms are established to compute the parameter m or ml exactly by a trial method, and also three approximate formulae to express J are proposed. The solutions are classified as five cases according to the characteristics of the spring system and the type of the wave form of the vibration. The frequency responses and some salient features of the solutions are examined and illustrated generally. The numerical results of J(ν) are shown in tabular form, the relative accuracy of which is about 10-4.
