Abstract
In a parametrically excited system whose natural frequencies are pi, pj, pk, and the parametric excitation frequency is Ω, an oscillation of a subharmonic type occurs when the relation pi∼- Ω/2 holds and that of a combination type occurs when the relation pi + pj ∼- Ω/2 holds. When the restoring forces are linear, these oscillations are unstable oscillations. But it is known that, in a nonlinear system, the nonlinearity modifies the growth of the unstable vibration and results in the steady oscillation with finite amplitude. In this paper, the internal resonance phenomena in such a system with nonlinear spring characteristics are investigated. Especially, we treat the case where the relation lpi + mpj = npk holds but each natural frequency is not an integer multiple of another natural frequency. By theoretical analysis, we clarified the followings : the kinds of parametric excitation terms and nonlinear terms which have an influence on oscillations ; induction of oscillation due to internal resonance ; occurrence of the almost periodic oscillations ; and so on.
