Free vibration analysis of branched blades by the integrating matrix method

The integrating matrix method is applied to determine the free vibration characteristics of bearingless rotor blades containing multiple branches at the root. It is necessary to include the axial degree-of-freedom in this analysis to account for the differential axial displacements in the branches. The inclusion of the axial degree-of-freedom leads to a nonlinear problem to determine the tension coefficients in the branches. The integrating matrix method is again applied to solve this nonlinear problem. The eigenvalue problem corresponding to branched bearingless blades forms a propert Sturm-Liouville problem and the associated orthogonality condition between the eigenfunctions is identified. The method is validated through comparisons with existing methods.