Coursework description

This part of the coursework constitutes 50% of the final mark in the unit. The coursework centres on vibrations and aeroelasticity applications in aerospace context. The coursework is divided into 5 tasks. Each task contributes 20% to the overall mark for the coursework. Further marking information is provided in section Marking (page 3).

Each task must be answered on a single page of your individual reports. The final report covering this theme will consist of five pages dedicated to the technical tasks (see separate comments regarding appendices) . This assessment closes a 10cp worth component of Dynamics and Control of Linear Systems. With this credit weight, the component amounts to approximately 100 hours of your work overall. Within this context and assuming the nominal engagement with the unit, the coursework is designed to be completed during five days of individual work. Those students who wish to start with tasks 1-3 can read Appendix first to appreciate the context and to familiarise with the provided Matlab tool.

IMPORTANT: You must use the version of the Matlab App which can be downloaded from the folder assigned to  the August  Assessment  Information in DCLS 2025.  All  students  have  their  own  individual  aerofoil parameters to work with.

•    “briefly”, “brief statement”, “short paragraph”, etc. generally means two, three or maximum four

lines of text, more text is seen as the inability to offer a succinct observation or discussion point.

Marking:

•    Each task contributes 20% to the total 100%. In each task: 50% of the mark is derived from “Results” and 30% from “Discussion” in terms of their degree of completion and their technical quality; 20% of  the mark is derived from the organisation (e.g., layout, flow, clarity), technical delivery (e.g., figures,  tables, equations) and English style.

• Every report is checked against plagiarism.

• Do not use text of this coursework document or graphics in your reports.

Academic integrity and AI statement:

•    See “Using AI in Assessment” (https://www.bristol.ac.uk/bilt/sharing-practice/guides/guidance-on- ai/using-ai-in-assessment/). This is a Category 2 assessment with regard to the report production.

•    AI/generative tools can be used to explore the concepts and improve learning productivity.

•    The use of grammar tools to change phrases, sentences, paragraphs, structure, flow, etc. as well as the use of translation tools in similar context exceeds the scope of category 2 assessment.

•    Each task must be completed based on your own intellectual ability without collaboration with any human or machine third party.

•    All  resources  provided  in  this  theme  can  be  used  to  develop  the  tasks  whilst  adhering  to  the standards of academic integrity (e.g., referencing, quoting, etc.).

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. Clearly identify the results and units! Using a single sentence statement in each case, name the method used to determine each physical parameter.

•    The other shown Result 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 briefly describe the process (method) you used to identify the torsional damping of the aerofoil.

•    One paragraph in your Discussion should briefly introduce an academic paper or report from the real- world engineering context where experimental damping identification is of interest. Use Internet or other formal resources to find such work.

Guidance, suggestions, hints:

•    The  default  system  in  the   Matlab  App,  after  its  start,  is  2DOF  and  needs  to   be  modified  to approximate the 1DOF aerofoil system. This can be done by reducing the significance of the TVA part in the system (“a grain of sand glued to the surface of the wing”).

•    Use  suitable  free  or  forced  conditions  to obtain such  responses that  can  be  effectively  used to calculate the required parameters.

•    For each  FRF (or AfCh, see  later) use an appropriate number of the frequency points to show the specifics of the shape of the function. Typically, between 10 and 20 points suffices for such use.

• Note: based on how it is defined in the lecture notes, AfCh can be seen as a function that presents the specific steady-state response to any form of harmonic excitation. FRF is a special function which presents the steady-state harmonic amplitude of an output DOF across a frequency range normalised by the input load amplitude. Based on this, an FRF can be seen as the AfCh produced for the case with a single load with the magnitude equal to one.

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 (calculated for the initial values of the aerofoil and TVA parameter values); (2) any 1DOF AfCh for the aerofoil DOF identified in task 1. In this figure, use labels to annotate its important features. In around three sentences, describe the method to establish the 2DOF AfCh and the rationale behind the chosen number of the frequency points used to represent it.

•    The other shown Result should represent an example simulation which was used to determine one frequency point of the AfCh. In this figure, indicate the region which was used to determine the required information for the AfCh.

•    One paragraph in your Discussion should briefly (two-three sentences) describe the typical aerofoil- TVA motion pattern (i.e., the relationship between the vibration amplitudes and phases) associated with the higher of the two resonant peaks.

•    One paragraph in your Discussion should list two different sources of damping found or introduced in real vertical or horizontal aircraft stabilisers.

Guidance, suggestions, hints:

•    Use your own initial (default) 2DOF system configuration in the Matlab App, in combination with the suitable range of harmonic   inputs, to calculate the amplitude-frequency characteristics (AfCh functions) such that all important features are well described.

Task 3: Tuned Vibration Absorber (20% of 100%)

Specification: Tune the TVA such that it absorbs or suppresses the resonance in your own 1DOF system. Present the following Results and Discussion points:

•    The first figure in Results should contain the following information identified with the  help of the Matlab App: (1) any 1DOF AfCh reused from Task 1; (2) 2DOF aerofoil AfCh for the case where the undamped TVA mass is 5% of the equivalent mass of the aerofoil (see hints); (3) 2DOF aerofoil AfCh for the case where the TVA mass is 15% of the equivalent mass of the aerofoil (see hints) and 20% TVA damping (see hints).

•    The second figure in Results, use Matlab App to illustrate and compare the resonant 1DOF simulation with the 2DOF case featuring one of the tuned TVA. Using two or three sentences, describe the parameter and excitation setup used to run both simulations.

•    One paragraph in your Discussion should comment briefly on the influence of limiting the TVA mass on the 2DOF characteristics described in the first figure.

•    One paragraph in your Discussion should briefly introduce two different academic papers discussing applications of TVAs in aerospace context from the period after 2020.

Guidance, suggestions, hints:

•    Use your own initial (default) 2DOF system configuration in the Matlab App, in combination with the suitable range of harmonic   inputs, to calculate the amplitude-frequency characteristics (AfCh functions) such that all important features are well described.

•    To  determine the equivalent mass of the aerofoil,  use the concept of “radius of gyration” from Mechanics formulated between the aerofoil hinge and the TVA attachment point.

o Note: mass moment of inertia = equivalent mass × (radius of gyration)2, where “radius of gyration” is known because we know where the “equivalent mass” is located for the purposes of this comparison.

•    The “%-value TVA damping”  represents the damping ratio of the TVA spring-damper-mass system when in isolation from the primary system (aerofoil) and acting as a 1DOF system.