Flutter screening for complex modes

In applying flitter screening to complex modes, a similar approach is fol­lowed.

The rigid complex mode is described as a complex —instead of real— coef­ficient linear combination of the same three fundamental modes: the pressure perturbation on a generic complex mode (at a given IBPA and frequency) is de­rived by linearly superposing the three fundamental real perturbations solved for the generation of real mode flitter maps.

Note that the generic complex mode is assigned as the sum of two real modes in quadrature with a specified amplitude ratio. This non-unique description of the mode is converted into a unique complex coefficient linear combination of the three fundamental modes, and the complex mode pressure perturbation and the aerodynamic work are consequently derived. The aerodynamic work normalization is consistently extended from real to complex modes, through an appropriate “complex mode amplitude” (see appendix).

In the above described approach to complex mode screening no simplify­ing assumptions are introduced [Kielb et al., 2003]: all contributions to the aerodynamic work are taken into account (those combining the unsteady pres­sures generated by one harmonic component to the displacements of the same harmonic component, those combing the unsteady pressures generated by one harmonic component to the displacements of the other harmonic component, as well as the mean pressure contribution).

Moreover, since a complex mode is specified through four real parameters (two complex coefficient ratios) rather than two (two real coefficient ratios), a two-dimensional flutter map is not suitable for complex mode flutter stability assessment.

Hence, when dealing with complex modes, mode-specific outputs are gen­erated. In particular, for each prescribed complex mode:

1 the aerodynamic damping coefficient (at each IBPA and frequency for which input data have been provided),

2 the stability parameter (at each frequency for which input data have been provided),

3 the critical reduced frequency,

4 the aerodynamic damping coefficient at a specified IBPA (at each fre­quency for which input data have been provided), obtained by exploiting the aerodamp sinusoidal approximation,

5 the critical reduced frequency at a specified IBPA.