Aeroelasticity (EAS 6993)

Prof. Pezhman Mardanpour 

January 10th, 2016

  • General information


Here is where to find more information:

  • About the mandatory homework format, see section 10.
  • The statement of academic honesty, see section 11.
  • Lectures: Tuesday-Thursday 9:30 a.m. to 10:45 a.m., EC1107.
  • Office hours: Tuesday-Thursday 11 a.m. to 12 p.m.
, or with appointment
  • Office: EC 3464, Phone: 305-348-6103, Email:
  • Teaching Assistant, Mr. Ebenezer D. Adelowo, Email:


  • Topics to be covered in this course

The following topics to be covered in this course:

  • Mechanics Fundamentals
  • Uniform String Dynamics
  • Uniform Beam Torsional Dynamics
  • Uniform Beam Bending Dynamics
  • Approximate Solution Techniques
  • Static Aeroelasticity
  • Dynamics Aeroelasticity


  • Course objective for students
  • To have a qualitative understanding of structural dynamics and aeroelasticity, including the knowledge of what disciplines are involved
  • To know how to derive equilibrium equations or equations of motion, including boundary conditions, for idealized structural dynamics and aeroelasticity problems
  • To be able to apply the method of separation of variables in solving the partial differential equations which arise in structural dynamics and aeroelasticity problems
  • To be acquainted with the modal representation for structural dynamics and aeroelasticity problems
  • To be able to solve initial value problems in structural dynamics
  • To be able to set up and solve divergence problems for spring-restrained rigid wings and for flexible wings represented by beams
  • To have a qualitative understanding of flutter solution methods and of unsteady aerodynamics theories
  • To be able to set up and solve flutter problems for spring-restrained wing models


  • Lectures

The lectures will cover the theoretical foundations of structural dynamics and aeroelasticity, and the syllabus will be followed as closely as possible. Because of time limitations, some material may be covered quickly; you are expected to ask questions for clarification. If you do not ask questions, I will conclude that you understand the material. If you can learn the material without coming to class, more power to you. However, I will warn you that most students perceive this as a hard course. Do not expect to get by without a lot of work.


  • Grading Policy

The overall numerical grade for this course will be computed using the weighting factors shown in Table 1.

Homework Assignments %10
2 Quizzes %25
1 Final exam %40

Table 1: Grade weighting factors

 Extra Credit: There are three ways you can boost your grade if you are not satisfied with your performance on the quizzes:

First, there will be an optional computer project on Structural Dynamics and/or Static Aeroelasticity assigned around the time of the second quiz, and your grade on it may be used in lieu of one quiz grade. It will at best overwrite your lowest quiz grade. It will have three parts: (I) a write-up of the theory, (II) a computer program, and (III) a report.

Second, there will be another optional project assigned around the time of the second quiz, this one on Unsteady Aerodynamics. It can boost your bottom line by up to three points.

Third, you may turn in a complete and correct set of homework at the end of the semester (at the time of the final exam). If your final grade, with all other things considered, is within two points of the cutoff between two letter grades, then the homework set will be examined. If it is submitted on time and indeed found to be complete and correct, it will boost your grade by two points. Note that this can only help someone who is on the borderline between two letter grades. No partial credit will be considered and no late sets will be accepted. Do not ask.

  • Homework

Homework will be assigned on a weekly basis. Homework is assigned on Thursday lectures and is due the next Thursday, in class. Homework is a vital part of the learning process, and 10% of your final grade. To make sure no homework is forgotten, an aging factor will be built into the grading as shown in Table 2. Do not forget to use the mandatory homework format, see section 7.


Date homework is turned in Aging factor
On the due date actual grade
Up to the Monday after due date actual grade – 1/10
Up to the Wednesday after due date actual grade – 2/10
Never turned in 0/10

Table 2: Aging factor for homework


  • Quizzes and Final

Two one-hour quizzes will be held at the dates posted on the schedule below. Quizzes are closed book and closed notes, but open minds. Three crib sheets, hand written front and back, are allowed at each quiz.

The comprehensive final exam will be held on week of finals. The format of the final is identical to that of the quizzes, but five crib sheets are allowed.

  • Reference books

The text is Introduction to Structural Dynamics and Aeroelasticity, 2nd Edition by Hodges and Pierce, available at the bookstore. It will be followed with few deviations. I expect you to read the text associated with all the topics we are covering during the course of the semester. I expect you to come to class prepared to ask questions on material being covered at that time. I will consider any assigned reading material in the text as “fair game” for quizzes and the final exam, whether or not I cover it in lectures. For those interested in further enrichment, there are several well-known texts on the subject matter:

  • Roy Craig and Andy Kurdila, Fundamentals of Structural Dynamics (2nd edition), Wiley, 2006.
  • L. Bisplinghoff, H. Ashley and R. L. Halfman, Aeroelasticity, Addison-Wesley Publishing Co., Inc., 1955 (reprinted by Dover).
  • Y. C. Fung, An Introduction to the Theory of Aeroelasticity, John Wiley and Sons, Inc., 1955 (reprinted by Dover).
  • L. Bisplinghoff and H. Ashley, Principles of Aeroelasticity, John Wiley and Sons, Inc., 1962 (reprinted by Dover).
  • E. H. Dowell, E. F. Crawley, H. C. Curtiss, Jr., D. A. Peters, R. H. Scanlan and F. Sisto, A Modern Course in Aeroelasticity, 3rd ed., Kluwer Academic Publishers, 1995.
  • R. Wright and J. E. Cooper, Introduction to Aircraft Aeroelasticity and Loads, John Wiley, 2007.
  • P. Rodden, Theoretical and Computational Aeroelasticity, Crest Publishing, 2011.


  • Course Schedule
Week Dates Reading Assignments Homework
1 Jan. 12th – 14th Chapter 1 – 2: Art 2.1 – 2
2 Jan. 19th – 21st Chapter 2: Art: 2.3 – 4
3 Jan. 26th – 28th Chapter 2:   Art: 2.5 – 7
4 Feb. 2nd – 4th Chapter 3: Art: 3.1
5 Feb. 9th – 11th Chapter 3: Art: 3.1 – 2
6 Feb. 16th – 18st Chapter 3: Art: 3.3 – 4
7 Feb. 23th – 25th Chapter 3: Art: 3.5 – 6 Quiz 1
8 Mar. 1st – 3rd Chapter 3: Art: 3.6
9 Mar. 8th – 10th Chapter 4: Art: 4.1
10 Mar. 15th – 17th Chapter 4: Art: 1.1 – 2
11 Mar. 22nd – 24th Chapter 4: Art 4. 2
12 Mar. 29th – 31st Chapter 4: Art: 4.2 – 3
13 Apr. 5th – 7th Chapter 5: Art: 5.1 – 2 Quiz 2
14 Apr. 12th – 14th Chapter 5: Art: 5. 3 – 4
15 Apr. 19th – 21st Chapter 5: Art: 5.5 – 6
16 Apr. 26th – 28th Chapter 4: Art: 5.7
  • Mandatory Homework Format

The homework you turn in are a good measure of the quality of your work and the effort you put into a course. Make every effort to present your work in the best possible manner.

  1. Use engineering paper only. PRINT your name clearly on the TOP RIGHT-HAND corner of each and every page. Work only on one side of the sheets. STAPLE all sheets together.
  2. Be careful about neatness and being organized. Please use pencil and clean erasure, ink is not acceptable.
  3. Neatness counts, it is a sound approach to engineering.
  4. Clearly indicate your final results by putting a box around your answers.
  5. Do not forget to keep track of UNITS during your calculations.
    • It is a convenient way to uncover math errors.

    • Please indicate units for your final answers: a final answer without units is 
not an answer.
  1. Describe your solution process first:
    • Provide a sketch of the problem with all relevant information.
    • If applicable, draw a free body diagram.
    • Derive the equations of the problem.
    • Discuss your approach to solving them (analytical, numerical, etc.)
    • Provide expressions for all the results you are plotting.
    • Comment on the physical nature and significance of your answers.
    • Please do not give an answer that makes no sense! It clearly indicates you do not understand the material.
  1. A plot conveys abstract information in a graphical manner. A plot must be drawn with the help of a software package (Matlab, Maple, etc.). Freehand drawing is a sketch, not a plot. Consider the plot shown in Fig. 1.
    • Both x and y axes must be properly labeled; provide UNITS. If it is a non- dimensional quantity you are plotting, say so.
    • If more than one curve appears on the plot, make sure to clearly differentiate them. Use different line styles or symbols.
    • Provide a caption that explains what quantities are plotted along the x and y axes. If more than one curve appears on the plot, provide a legend to explain the meaning of each curve.
  2. If you are using a software package (Matlab, Maple, etc.) as a part of your solution process, include the input/output files to these packages as part of your submission.

Figure 1: Trajectory of the particle: ignoring air friction (solid line); with friction coefficient k = 0.001 kg/m (dashed line); and k = 0.002 kg/m (dashed-dotted line).


  • Statement of Academic Honesty

The honor system is assumed.

  1. You may, and are encouraged to discuss how to work out the problem sets with your classmates. Classmates are an excellent source of information. There is an obvious difference between a constructive discussion about a homework with a friend, and copying your friend’s homework.
  2. Of course, copying is not permitted.
  3. For more information see the FIU Academic Honor Code.