Response of a nonlinear two-degree-of-freedom system to a horizontal harmonic excitation

An elastic structure containing a fluid subjected to a horizontal sinusoidal excitation is investigated. The system is found to include cubic nonlinearities. The system response is determined by using the multiple scales asymptotic approximation method. The method predicts that primary resonances may occur when the excitation frequency, Ω is close to either the first mode natural frequency, ω1, or the second mode natural frequency, ω2. The system behavior under the fourth order internal resonance condition (ω2 ≈ 3ω1) is predicted. The system response under conditions of primary resonances (Ω ≈ω1 and Ω≈ω2), together with internal resonance is also considered. Other features, such as amplitude jump phenomenon and chaotic-like response have been observed. Two possible responses have been found when Ω is near ω2 = unlmodal response and autoparametric interaction response. The boundaries of these two motions are defined in the excitation amplitude - frequency plane. Moreover, the so called "static attractor" is also observed.