Parametric study on internal resonances for a simplified nonlinear blade model

Abstract

This article proposes to determine and identify the physical contributions that drive the internal resonance between the bending and torsion modes of a blade. The blade is modeled as a nonlinear beam including warping, twist and pre-bending, and a discretization scheme based on a Rayleigh–Ritz approximation is performed. The modal properties of the model are compared and validated using beam theory and finite element modeling. Several configurations of the model allowing the occurrence of an internal resonance between the first torsional and the second bending modes are considered. The frequency responses near the second bending mode are obtained through the Harmonic Balance Method coupled with a branch switching algorithm to locate and track bifurcated branches related to internal resonances. Attention is paid to the identification of the geometrical nonlinear terms that enable the appearance of an internal resonance. With the help of a multiple scale analysis, it is shown that it is essentially driven by a small set of coupling parameters involving bending and torsion displacements of the commensurate modes. It is also observed in a rotating situation thanks to the hardening of the bending mode.