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STRUCTURAL DYNAMICS AND AEROELASTICITY Prof. Giuseppe Quaranta, July 03, 2023 Exercise 1: Static aeroelasticity Consider a swept wing whose geometry is shown in the Figure. The chord ¯ c is constant, and ¯L is the span. Let Λ be the backward sweep angle. The struc- tural behaviour of the wing can be modelled using a beam with flexural stiffness EJ (¯y) which varies in span and torsional stiffness which can be con- sidered infinite. The beam axis is at 40% of the chord. At the tip of the wing, there is a rigid mov- able surface of chord ¯c and span ¯b whose rotation around the beam axis can be controlled by an ideal actuator. Use as an aerodynamic model the strip theory for an incompressible flow. Coefficients CLα must be considered known in the aerodynamic ref- erence frame. 1.a) Show a method to estimate the dynamic pres- sure of control reversal qR, using Ritz Galerkin approximation with a well-chosen shape func- tion. 1.b) (Optional) Illustrate how the introduction of a finite torsional stiffness GJ(y) may modify the solution. Exercise 2: Dynamic stability Consider the horizontal tail structure shown in the Figure. A beam of length L having bending stiffness EJ , torsional stiffness GJ, mass per unit length mt and polar moment of inertia per unit length It, all constant along the beam. At its free-end, there are two lifting surfaces, to be consid- ered rigid, of chord c, span b and mass per unit area mw, connected by two springs of rotational stiffness K that connect the end of the beam with the lifting surfaces. The rotation axis of the lifting surfaces is at 50% of the chord. The structure is invested by a flow having an asymptotic velocity U. Consider an incompressible flow and adopt the linearized quasi-steady strip theory approximation as aerodynamic model (…