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Natural frequencies and mode shapes of a thin plate Application: Airplane wing Introduction to Vibrations Figure / The boundary conditions: . The side AD is clamped (fixed) • The 3 other sides are free Characteristics of the thin plate: Length: L-1 m • Width: d-0.4m • Thickness: h=5mm (0.005m) . Young's modulus: E-2.1 El Pa . Poisson Ratio: v=0.3 • Density: p=7800 kg/ml What to do?: 1- Determine the 5 first Natural frequencies and the 3 corresponding Modal Shapes of the rectangular thin plate (Figure 1) 2- Do The same for a simplified airplane wing (Figure 2). Add a sort of an engine under the plate. The engine is a simple empty cylinder placed at any distance from the fixed side (0.3m or 0.4m or 0.5m...) with the same characteristics (also same thickness) as the plate and a diameter of 0.15m. (Optional: You may, instead create a more realistic wing with you own dimensions and geometry) 3- Print a report with an Introduction, Results and Conclusions (3 to 10 pages) and hand it in before the deadline ........NO EMAILS please. Figure 2