23 Development and Validation of Data Processing Techniques for Aircraft Ground Vibration Testing 227 a b Fig. 23.1 Conventional performed sweeps during a two points excitation sweep test. (a) Sweep 1: symmetric sweep. (b) Sweep 2: antisymmetric sweep frequency band and for all the sweeps that are executed, while their relative phase changes from a sweep to another in order to satisfy the second condition. Figure 23.1 shows the conventional relative phase scheme that is adopted for a two points excitation configuration: the first sweep is symmetric because the forces are equal both in amplitude and phase, while the second sweep is antisymmetric because the right wing force, i.e. the reference input, maintains a 0◦ phase while the left wing force switches its phase to 180◦, which means that it has an opposite direction with respect to the one of the reference input. This resulting configuration matches also the necessity of an excitation able to emphasize symmetric and antisymmetric modes of the aircraft. Indeed, tail and wings modes, that are mainly symmetric or antisymmetric with respect to the fuselage position if a structural symmetry can be recognized, are considered to be the most interesting modes to be investigated. 23.3 Virtual Driving Point Method for a Two Points Excitation Configuration The Virtual Driving Point (VDP) method is based on the identification, for each sweep that is performed with multi-point excitation, of a virtual force and a virtual response. Both of them are computed starting from the measured forces and responses of the two actual driving points of the system, i.e. the two physical points where the excitation is applied through the two shakers. Thanks to this procedure, each single sweep can be individually analyzed and a set of system’s FRFs, that are then used as starting point for the modal analysis, can be extracted. Therefore, each sweep identifies a specific mode set that, in most of the cases, has to be combined with the others in order to obtain the final mode set of the system. 23.3.1 Adopted Procedure for the VDP Method Application The VDP mathematical formulation involves inputs and outputs frequency spectra, which can be respectively expressed as in Eqs. (23.4) and (23.5). {F (ω)}= F1 (ω) F2 (ω) = |F1 (ω)|e jϕ1 |F2 (ω)|e jϕ2 (23.4) {Y (ω)}= ⎧⎪⎨ ⎪⎩ Y1 (ω) . . . YNo (ω) ⎫⎪⎬ ⎪⎭ (23.5) Here Y1 and Y2 are assumed to be the driving points measured accelerations, F1 is the reference input and F2 is the delayed input, where the delay is ϕ =ϕ2 −ϕ1. The computational steps for the VDP method application start from calculating the
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