On the generation of a set of accurate numerical modal functions for use in the aeroelastic analysis of flexible rotor blades

A comparison is presented of three methods for the generation of numerical, modal approximating functions for use in modal Lagrangian analysis of rotating flexible blades. The methods considered are those based on the use of uniform beam/bar eigenfunctions, smooth bending moment or torque modes, and modes generated by recourse to one stage of the Stodola method. For blades which are highly non-uniform in their specific stiffness and inertial properties, and where the objective is to use a small number of approximating functions, consistent with accurate determination of eigen-solutions in the fundamental spectrum, it is demonstrated (as is well known) that direct use of uniform system eigenfunctions is unsatisfactory. On the other hand, it is demonstrated that the use of smooth bending moment modes, even in cases where the variations in sectional inertia properties are very large, can produce excellent results. The use of ‘Stodola modes', however, is shown to offer the all-important advantage of enhanced convergence rate in all cases considered.