Q1.
(i) State if the following statements or true or false: (a) Quasi-steady aerodynamic theory is independent of reduced frequency.
sinA is a suitable assumed shape for representing a 1D clamped-free member in bending.
(c) Theodorsen’s theory accounts for velocities induced by trailing wake.
(d) Theodorsen’s theory accounts for viscous boundary layers. [4]
(ii) Provide brief answers (in 1 or 2 sentences) for the following questions:
(a) What are the considerations when choosing an assumed shape for a problem? [4]
(b) Why is an iterative approach such as the ‘k method’ or ‘p-k method’ required for flutter calculation? [4]
(c) Why is wing kinetic energy not considered in setting up the aeroelastic model (through Lagrange’s equations) for control reversal? [4]
(d) What is the physical mechanism behind aileron control reversal? [4]
Q2.
An aerofoil undergoes harmonic oscillations in pitch and heave. At a certain instant in time, the value of lift calculated from quasi-steady aerodynamic theory is 𝐿 = 5000𝑁. The reduced frequency of oscillation is 𝑘 = 0.5 and Thedorsen’s function for this value is 𝐶(𝑘) = 0.5979 − 0.1507𝑖 Calculate the circulatory lift from Theodorsen’s theory at this same instant, and the difference in magnitude and phase in comparison with the quasi-steady lift. [10]
Q3.
A wing contains two ailerons that together total the entire semi-span of the wing. Using a linear assumed shape for wing torsion, determine the size of the two parts such that they each give the same root bending moment at the operating condition specified below. Wing properties: 𝑠 = 4m, 𝐶𝑙𝛼 = 2𝜋, 𝐶𝑙𝛽 = 𝜋[20]
Q4.
For a non-uniform tapering member of length 𝑠, built-in at one end and free at the other, with mass per length and flexural stiffness distributions use a quadratic assumed shape to estimate the fundamental natural frequency in bending. [25]
Q5.
Determine the divergence speed of a fixed-root tapered rectangular wing of semi-span 𝑠 and chord and torsional rigidityUse a linear assumed shape and let the root incidence of the wing be 𝜃0 .
Compare the divergence speed for this tapered wing with that of a rectangular wing.[25]
Commentaires