Abstract
The steady-state response of spatially modulated doublet modes that occur in low count flexible bladed disks is investigated for the case in which the structure is driven by a harmonic traveling wave excitation source. Finite element simulation and modal testing of prototypical bladed disk structures demonstrate the presence of particular wavenumbers, beyond the base number of nodal diameters, which contaminate and distort the appearance of certain doublet modes. The manner in which the natural frequency and wavenumber content of such modes shift and split as functions of the number of blades and their span angle is discussed in the light of a companion perturbation analysis for rotationally periodic structures. Resonance conditions are established and verified through simultaneous measurements made with a spin test stand using sensors that are placed in the rotating (structure) and stationary (excitation) frames of reference. The traveling wave response components of a repeated frequency doublet mode are shown to propagate either in the same or opposite direction as the excitation source, depending on whether certain algebraic relationships between the excitation order, the base number of nodal diameters, and the contamination wavenumbers are satisfied. To the extent that such components can travel at different phase speeds and directions relative to one another, the placement of sensors on the structure can be optimized to best measure the response amplitude. Conversely, other placements can result in sub-maximal measurement of peak vibration amplitude over the structure.
