Nonlinear Normal Modes-Related Isolated Branches of Subharmonic Solutions for Forced Response Blade-Tip/Casing Contact Problems

This article investigates the emergence of isolated branches of solutions for blade-tip/casing structural contact configurations by means of a numerical procedure relying on Melnikov's energy principle. This study is carried out on the open fan blade model NASA rotor 67 in order to promote the reproducibility of the results. The blade is subjected to an harmonic forcing so as to initiate rubbing interactions. Contact is modeled in the frequency domain by the dynamic Lagrangian frequency-time harmonic balance method (DLFT-HBM) that accounts for vibro-impact as well as dry friction. This paper employs an isola detection procedure that was shown to give accurate results on such highly nonlinear applications. Several types of harmonic forcing are applied to the blade in order to observe subharmonic (i.e., with a fundamental frequency expressed as a fraction of the excitation frequency) isolated solutions. The existence of these solutions is shown to be related to nonlinear normal modes that feature lower periodicities than the excitation. The periodicity of the solutions is assumed to be linked to the periodicity of the nonlinear normal modes from which these solutions emerge. In some configurations, it is shown that nonlinear periodic solutions exist in the form of isolated branches while the main predicted response remains within the linear domain. This behavior is particularly detrimental since numerical strategies tackling nonlinear problems are usually not put to use when the response of the system is expected to be linear. The existence of such solutions is cross-checked by means of reference time integration simulations. Finally, an excitation of random shape is applied to show that this complex phenomenon persists for nonsimplified excitation shapes.