A 3D Theodorsen-based rotor blade flutter model using normal modes

This thesis presents a fully coupled, quasi-3D analysis of rotor blade flutter that can accommodate forward flight conditions. The rotor blade is modeled as a uniform beam, taking the average characteristics of a real blade between 20% and 90% of its length. Applying Rayleigh's method, the first few bending and torsion normal mode shapes and natural frequencies are determined, and then adjusted for the rotating case. With this data, force and moment equations of motion are developed using Lagrange's equation along with a normal mode analysis. Theodorsen coefficients are calculated over a range of forward velocities (input as reduced frequencies) for a specified number of elements along the blade model. Incorporating these coefficients into the equations of motion, a square matrix is generated from which complex eigenvalues can be derived. These eigenvalues provide the aeroelastic natural frequencies and damping coefficients for each coupled mode. The forward velocity at which one of the modes produces a positive damping coefficient gives the value of reduced frequency for the flutter point. The resulting forward speed and blade tip speed can then be determined.
http://archive.org/details/adtheodorsenbase109454580
Lieutenant, United States Navy
Approved for public release; distribution is unlimited.