Flutter screening for real modes

Before applying flitter screening to complex modes, real mode screening has been implemented, through the integration of LARS with a specific pro-

gram developed at Department of Energy Engineering (University of Florence). This program is called INDIAN (INtegrated & Distributed ANswer).

A detailed description of real mode flutter screening is not the aim of this paper, but the procedure will be briefly reviewed, because it represents the baseline scheme in the development of complex mode flitter screening.

An arbitrary real rigid vibration mode can be described as a real coeffi­cient linear combination of three fundamental real modes, and the aerodynamic work can be expressed as a quadratic form of these coefficients. Once the 3 x 3 work matrix has been derived, the evaluation of the aerodynamic work for any real mode is straightforward and very efficient.

The aerodynamic work is then normalized to obtain the aerodynamic damp­ing coefficient. This normalization is defined through a (squared) vibration amplitude, identified in such a way to achieve consistency with the traditional definitions of damping coefficient in the two particular cases of pure bending and pure torsion. In the appendix a fully consistent normalization is derived, al­ternative to that proposed by Panovsky and Kielb [Panovsky and Kielb, 2000].

In the LARS-INDIAN based screening procedure:

1 aeroelastic calculations are carried out on two pure bending modes along orthogonal directions and one pure torsion mode, selected as fundamen­tal modes, at prescribed interblade phase angles (IBPAs) and vibration frequencies, covering the respective ranges of variation;

2 fundamental perturbations are combined, so that the work and aerody­namic damping for any arbitrary torsion axis location can be derived;

3 the generation of several flutter maps, applicable in real mode flitter screening, is allowed, namely:

■ aerodamping maps, providing the aerodynamic damping coeffi­cient as a function of torsion axis location —or bending direction— for a given IB PA and vibration frequency,

■ stability maps, providing the stability parameter (defined as the minimum of the aerodynamic damping sinusoidal approximation over the range of IB PA variation) as a function of torsion axis lo­cation —or bending direction— for a given frequency,

■ critical reduced frequency maps, providing the reduced frequency below which the stability parameter becomes negative as a function of torsion axis location —or bending direction—.