Task 1: Single degree-of-freedom analysis (20% of 100%)
Specification: Use the provided Matlab app to find the physical parameters of the aerofoil (mass moment of inertia of the aerofoil about its hinge, torsional damping, torsional stiffness). Present the following Results and Discussion points:
• The main figure (graph) in Results should contain (1) the 1DOF FRF obtained using the harmonic excitation in the Matlab app, overlayed with (2) the FRF calculated analytically using the physical parameters, further combined with the information indicating (3) the 1DOF undamped natural frequency.
• The other shown Results should represent the summary table with the found parameters and one additional auxiliary figure illustrating (any) one of the methods used during parameter identification.
• One paragraph in your Discussion should describe the method you used to identify the mass moment of inertia of the aerofoil.
• One paragraph in your Discussion should briefly describe a possible way in which the torsional stiffness could be measured on the real vertical stabiliser or aerofoil.
Guidance, suggestions, hints:
• Recommended layout: Results section 2/3 A4 page, Discussion 1/3 A4 page.
• The default system in the Matlab app, after its start, is 2DOF and needs to be modified to approximate the 1DOF aerofoil system by reducing, suitably, the significance of the TVA part in the system.
• Use suitable input conditions (forced, free vibrations) to obtain such responses that can be used to calculate the parameters, e.g., LogDec, static or slow deformation, very high frequency excitation.
• For each FRF (or AfCh in some later tasks) use a suitable number of the frequency points to show the specifics of the function. Typically, between 10 and 20 points suffices for such a demonstration.
• Recommended resources: lectures 3, 4, 7, 8.
Task 2: General two degree-of-freedom analysis (20% of 100%)
Specification: Use the provided Matlab app to calculate 2DOF system AfCh and present the following Results
and Discussion points:
• The single main figure (graph) in Results should contain the following information identified with the help of the Matlab app: (1) the initial 2DOF AfCh for the aerofoil DOF and (2) 2DOF AfCh for the TVA DOF (calculated for the initial values of the aerofoil and TVA parameter values); (3) 1DOF AfCh for the aerofoil DOF; (4) the information indicating the calculated 2DOF undamped natural frequencies (e.g., labelled vertical lines).
• The other shown Results should represent the summary table with the values of the undamped natural frequencies (also visualised in the main figure).
• One paragraph in your Discussion should briefly discuss the role of the aerofoil and TVA damping on the shape of the calculated AfCh functions.
• One paragraph in your Discussion should comment briefly on the typical aerofoil and TVA motion patterns associated with the 2DOF AfCh function peaks.
• One paragraph in your Discussion should briefly describe the typical sources of damping in real vertical or horizontal aircraft’s stabilisers.
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