a 2024 07 05 solution

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STRUCTURAL DYNAMICS AND AEROELASTICITY Prof. Giuseppe Quaranta July 05, 2024 Exercise 1: Static aeroelasticity Consider the structure in the figure that is composed of an inclined beam with an angle Λ that supports a rigid rectangular wing that has the chord c aligned with the flow speed V . The support beam of length L, bending stiffness EJ , and torsional stiffness GJ is clamped at one end and connected to the mid- chord of the wing at the other end. Consider the wing immersed in an incompressible flow, and CLα as the lift-slope coefficient. 1.a) Develop a simple model to compute the first divergence dynamic pressure. 1.b) Compare and comment on the cases when Λ is 90° , 0° , and −90° . Exercise 2: Dynamic stability Consider the symmetric rigid aircraft model suspended at the ceiling of a wind tunnel through four springs as shown in the figure. The main wing chord is c and the span is 2 b. It has a mass per unit surface equal to mw uniform, and is connected through a rigid rod of negligible mass to a rigid tailplane of chord c and span b. The center of gravity of the tailplane is at 25% of the chord; the total mass is MT and the total moment of inertia along the axis at 25% of the chord is IT . The stiffness of the springs is k or 3 k as shown in the figure. The structure is immersed in an incompressible flow of speed V and the lift slope coefficient of the lifting surfaces is CLα. Use the strip theory with quasi-steady approximation to compute the aerodynamic loads. 2.a) Write the equations of motion to investigate the stability of the aircraft model considering only the symmetric degrees of freedom. 2.b) Present a methodology to investigate the dynamic stability. 2.c) Consider now the case when an impulsive moment is applied to the aerodynamic center of the main…