PSI - Issue 24

Corrado Groth et al. / Procedia Structural Integrity 24 (2019) 875–887

884

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C. Groth et Al. / Structural Integrity Procedia 00 (2019) 000–000

Table 2: MAC table for the front wing assembly

Baseline

0.915 0.379 0.082 0.300 0.397 0.982 0.102 0.343 0.494 0.503 0.135 0.445 0.574 0.540 0.158 0.492

Updated

using cubic splines to interpolate the Aerodynamic matrix known at discrete velocities and reduced frequencies. This analysis confirms a flutter instability. By plotting the norm g of the Real and Imaginary parts of the complex pole s = R e ( s ) + j I mag ( s ) = g 2 π f + j 2 π f with respect to the velocity V , it is possible to highlight the crossing of g on the positive semi-plane. V - f and V - g diagrams are shown in figure 6. The critical velocity obtained for the baseline geometry is 47.6 m / s with a frequency of 65.7 Hz. Similar remarks can be done by examining the results, obtained with the sti ff ened configuration, employing the first four vibrational modes. Also in this case the first mode is responsible for the instabilities, occurring at 68.1 m / s and at a frequency of 73.1 Hz. In figure 7 the V - f and V - g diagrams are shown, highlighting the instability mainly associated to the first assumed mode shape. Considering the reached flutter condition with flutter frequency ω cr and flutter speed V cr , the (four) components of the related critical eigenvector { w cr } T = { w 1 cr , w 2 cr , w 3 cr , w 4 cr } can be evaluated by the omogeneous problem � − ω 2 cr [ M ] + [ K ] − 1 2 ρ V 2 (19)

   = 0

cr [ H ( ω cr , V cr )] �   w cr 1 w cr 2 w cr 3 w cr 4

These four numbers are able to quantify the participation of each structural modes to the flutter critical vibration: in this case a considerable value obtained for the component w 1 cr has indicated the first structural mode as the main one involved in the flutter vibration. In figure 8 the flutter deformation for the sti ff ened geometry is shown amplified 300 times.

4. Conclusions

In this paper the flutter analysis of the front wing splitter mounted on the 2001 Le Mans Prototype car by Dallara (LMP1) was presented. By using high fidelity fluid dynamic and structural models, a modal superposition coupling was employed using Radial Basis Functions (RBF) morphing. The vibration modes of the baseline front wing, and of a similar model sti ff ened using a spider structure, were excited employing a finely-tuned smoothed step function, carrying transient CFD simulations in order to build a suitable linearized unsteady ROM for aerodynamics. Thus,

Fig. 5: LMP1 Pressure coe ffi cient contours for the 50 m / s case