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STRUCTURAL DYNAMICS AND AEROELASTICITY Prof. Giuseppe Quaranta January 15, 2024 1 Exercise 1: Static aeroelasticity Consider the structure shown in the sidefigure. A horizontal beam of length Land with uniform bending stiffnessEJ fixed on the ground is connected at one tip with two movable surfaces that can rotate about theEAaxis. The movable surfaces have both a chordcand a sur- faceS, and they are initially rigidly con- nected through the rigid rodr. Two tor- sional springs of stiffnesskconnect the rotation of the beam tip to the rotation of the movable surfaces. The two surfaces are immersed in an asymptotic incom- pressibleflow of speedUand the lift- curve slope isC Lα. The aerodynamic cen- ter axisACis at a distanceefrom the rotational axis. 1.a) Determine the divergence dynamic pressure using a single well-chosen bending shape function. 1.b) Determine if it is possible to move theEAaxis so that the system becomes divergence-free. Justify your answer. 1.c) What happens if the two movable surfaces are separated so that each one rotates independently? Exercise 2: Dynamic stability Consider a wing of spanband chordc, connected to a support that is composed of a rigid arm of spanL/2 connected to a perpendicularflexible beam of lengthL, bending stiffnessEJ, torsional stiffness GJ, mass per unit spanmand moment of inertia per unit spanI θ. The wing has a uniform mass per unit surfacem w and is immersed in an incompressibleflow with speedU. The rigid arm is connected at half of the chord of the wing and the aero- dynamic center is atc/4. Adopt a steady aerodynamic modelL=qcC Lαα. It is re- quired to: 2.a) Write the equations of motion using the Ritz-Galerkin method to approximate the problem. 1In the original version of this text there were some errors in thefigures. These errors…