Development of a New Stability Method with Applications to Rotary Wing

A new stability approach, termed the indirect eigenvalue method, blends the benefits of a direct eigenvalue approach with the versatility of time-marching schemes commonly used by high-fidelity methods such as computational fluid dynamics (CFD). The indirect method relies on an accurate estimate of eigenvectors of interest, and both timeinvariant and time-periodic formulations are developed. The use of simple harmonic motion to extract information from time-domain simulations such as CFD is shown to have a theoretically bounded error for time-invariant systems that is well within engineering accuracy for lightly damped systems. A time-invariant application employing CFD corresponding to rigid lag is examined and compares well with time-domain perturbation results. By examining the spatial distribution of damping, the foundational cause of the rigid lag damping is found to grow cubically with span and to be dominantly driven by viscous forces acting on the blade. A time-periodic verification example is developed employing simplified blade flapping equations. The indirect method is shown to be reasonably error-tolerant for timeperiodic problems, provided the eigenvectors are accurate.