## 5 Structural Design and Systems Integration
### Aeroelastic Trade-Off  
As for any safety-critical device, a preliminary assessment of morphing winglet on aircraft aeroelastic stability was judged to be extremely relevant to avoid the consolidation of an unsafe, and therefore unflyable, structural layout.  
Flutter analyses were carried out in two consecutive phases; at first, trade-off investigations were addressed to establish the maximum allowable weight of the winglet structure.  
To this aim, the entire device was modelled as a lumped mass placed at the wing tip; starting from the typical mass value of a conventional arrangement, the winglet mass was progressively increased until bending-torsion flutter of the wing was induced within the flight certification envelope (i.e., at a flight speed lower than 1.25, the aircraft dive speed VD). Bending/torsion flutter speed was estimated by referring to the Molyneux equation [49] and to the wing's natural frequencies resulting from the model described in Section 2.4.1; both symmetric and anti-symmetric coupling mechanisms were considered.  
It was found that only the flutter due to the coalescence of anti-symmetric wing bending and torsion was sensibly affected by the winglet mass increase (Figure 23); in order to assure aircraft flutter clearance, the overall mass of the imposed morphing winglet did not exceed the value of 90 Kg.  
The preliminary structural design of the morphing winglet (Section 5.1) was carried out under this relevant inertial constraint and, once completed, a new loop of analyses was performed to verify the clearance from any other type of flutter induced by unstable couplings of winglet and wing modes.  
The finite element model of the morphing winglet described in Section 5.3 was condensed into a dynamically equivalent set of beams, which were integrated into the overall aircraft aeroelastic model to replace those used for the simulation of the conventional winglet (Section 2.4.1). Winglet movables were also modelled through equivalent beams, and the rotation around their longitudinal axis was constrained by means of grounded springs reproducing the stiffness of the actuators in power-on mode.  
Figure 22: Finger-like mechanism of the winglet morphing tab.  
The aircraft aeroelastic stability equation was solved in the space of modal coordinates and in the frequency domain; the critical speeds were evaluated by means of PK-method [50] under the following assumptions:  
* Association of the theoretical elastic modes up to 60 Hz;
* Modal damping conservatively set to 1.5% for all the elastic modes;
* All moveable surfaces in control-fixed attitude;
* Sea-level flight altitude;
* Flight speed range: (0: 200 m/s) 200 m/s being equal to 1.25\({}^{\circ}\)V\({}_{\text{D}}\) as for certification requirements.  
All flutter calculations and the elaboration of Vg plots were made in SANDY software environment [51].  
A flutter due to the coupling of winglet movable harmonics and winglet bending/torsion was found at a critical speed of nearly 200 m/s (Figure 24). The flutter dynamics were proven to be induced by a typical underbalanced behaviour of the movables. To increase the margin of safety with respect to flutter, the degree of mass-balancing of each movable was then increased up to 0.7, which successfully led to a first critical speed of nearly 210 m/s (Figure 25). In such a configuration, a further flutter speed was also detected; nevertheless, since it was much higher than 200 m/s, it was considered not critical for the safety of the reference aircraft.  
Figure 23: Flutter Speed diagram with various winglet mass.