Experimental and theoretical investigation of superharmonic resonances in a planar oscillator under angular base excitation

This paper explores the complicated dynamic behavior of a mechanical oscillator under harmonic angular excitation. The motivation behind this work comes from the nature of the actuation produced by high-performance dither motors. A lumped-mass model, which captures the primary and the 1 : 2 superharmonic resonances observed on an analogous experimental test setup, is put forward. The equations of motion governing the dynamics of the model are derived and are found to comprise both parametric and direct forcing terms. The governing equations are solved analytically using the generalized harmonic balance method and numerical integration. The method of multiple scales is utilized to obtain closed-form expressions that relate the system parameters to the oscillation amplitudes in the vicinity of the direct and the 1 : 2 superharmonic resonances. It is found that eccentricity plays a vital role in the occurrence of the resonances. Besides, the relationship between the excitation amplitudes and the resulting oscillations for the direct and the superharmonic resonances are dissimilar. A few salient differences between classical (rectilinear) and angular base excitation mechanisms are pointed out.