Internal resonance in a nonlinear two-degree-of-freedom system. (1st Report, Subharmonic and superharmonic oscillation with no coincidence of resonance points in a system whose natural frequencies are at the ratio of 1:2).

Abstract

The influences of the internal resonance on the subharmonic oscillation [3p2] and the superharmonic oscillations [p1/2], [p1/3], [p2/3] in a nonlinear two-degree-of-freedom system whose natural frequencies, p1 and p2 are at the ratio of 1:2 are discussed. By the theoretical analysis, we clarified the following : (a) The kinds of nonlinear terms which have an influence through the internal resonance are different among these nonlinear forced oscillations. (b) In the cases of the oscillations [3p2] and [p2/3], the stationary solutions where two modes coexist appear in addition to those which appear in the system with no internal resonance. The resonance curves of the former bifurcate from those of the latter. (c) In the cases of the oscillation [p1/2] and [p1/3], the other mode always appears, and only the solutions where two modes coexist appear. (d) Almost periodic oscillations are not obtained in every oscillation.