Abstract

It is known that isolated frequency response branches (isolas) can occur near primary resonances under modal interactions or nonlinear damping. The present work demonstrates how emergence and vanishing of such isolas can be systematically analyzed in an experiment. Feedback control of the phase is employed to track the phase-resonant backbone curve. In addition, the amplitude of the response is controlled, as the excitation level undergoes turning points in the presence of an isola. The acquired data indicates what excitation levels lead to the formation of an isola / its merging with the main branch. Some further analysis of the data permits to characterize possible internal resonances and amplitude-dependent damping. To assess the proposed method, a test rig is considered which involves two similar cantilevered beams undergoing soft collisions via a unilateral spring. A simplified model, which relies on linear modal damping and a massless unilateral spring, suggests that isolas should appear as a result of internal resonances. In contrast, the experiment shows an isola due to nonlinear damping. More specifically, the damping ratio first increases substantially due to the frictional dissipation in inevitable joints. Subsequently, the unilateral interactions scatter energy to other modes (in a non-resonant way), which have much lower damping. This leads to a sudden drop of the effective damping ratio with the amplitude, and leads to the formation of an isola.

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