**Aerospace Engineering 4220-A:** **Introduction to Structural ****Dynamics and Aeroelasticity**

**School of Aerospace Engineering**

**Georgia Institute of Technology**

Prof. Dewey H. Hodges

Office: Weber 200-C; Phone: 4-8201; Fall 2018

E-mail: dhodges@gatech.edu

**Time and place**: The class hours are 12:00-1:15 p.m., Tuesdays and Thursdays, and the place is Guggenheim 442.

**Office Hours**: My office hours are Tuesdays and Thursdays, 1:30 – 3:00 p.m. The teaching assistant is Tianchen Cai <tcai30@gatech.edu> who has office hours in ESM, room 203B on Mondays and Wednesdays, 1:30 – 3:00 p.m.

**Text**: The text is *Introduction to Structural Dynamics and Aeroelasticity, 2 ^{nd} 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 cover 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*. For those interested in further enrichment, there are several well-known texts on the subject matter:

**assigned reading material**in the text as “fair game” for quizzes and the final exam, whether or not I cover it in lectures- Roy Craig and Andy Kurdila
*, Fundamentals of Structural Dynamics*(2^{nd}edition), Wiley, 2006. - R. 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). - 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. L. Bisplinghoff and H. Ashley,
*Principles of Aeroelasticity*, John Wiley and Sons, Inc., 1962 (reprinted by Dover). - J. R. Wright and J. E. Cooper,
*Introduction to Aircraft**Aeroelasticity and Loads*, John Wiley, 2007. - W. P. Rodden,
*Theoretical and Computational Aeroelasticity*, Crest Publishing, 2011.

**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. There has been a tendency for some seniors, particularly when they are enrolled design, to cut 4220 classes. 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. Note:

- Please arrive class on time.
- Tablets and laptops are allowed for taking notes only.
- No eating
- No sleeping
- No excessive talking
- No texting
- No reading of newspapers, magazines, or Internet articles
- No puzzles or games

**Examinations**: There will be two quizzes and a final examination. The quizzes will count 25% each, and the final will count 40%. On exams you may be asked to “show that” certain results are obtained. If you try to deceive me into thinking that you have done something that you really have not, and I catch it, you will get zero credit for that problem on the first offense, zero on the test on the second offense, and reported to the Dean of Students on the third offense for an **honor code** violation. Note:

- Should you miss class on a quiz day, a make-up quiz will only be given if I receive a request from the Office of the Dean of Students to excuse a medical emergency or illness or if you have a death in your immediate family. In the latter case, you must notify me before the quiz either by email, by phone, or by voicemail.
- On test papers you must use the notation used in the course.
- Explain what you are doing at each step, because credit is given mainly for the method, not the answer.
- Put a box around your final answer to help me grade your work.
- Write only on the front side of each sheet you turn in with a test.
- If you continue to write once time is called, you could be charged with a violation of the Honor Code.
- If you attempt to turn the test in after I walk out, you could be charged with a violation of the Honor Code.

**Homework**: There will be homework problems assigned (1 or 2 per week). These will be collected and graded. They will count 10% of your grade. That’s a miniscule part of your grade. Understand that these homework sets are primarily assigned to help you learn. Here is wisdom! If you can work the assigned problems on your own, it is likely that you will also be able to work the problems given on the quizzes and on the final exam. If you choose dishonest routes, such as copying solutions from fraternity files, copying down solutions obtained from a group of your classmates, etc., you might make good homework grades. Because homework counts so very little, that will be the extent of your benefit. If you never learn how to work the assigned problems on your own, it’s likely that you will fail the tests. See http://www.sciencenews.org/view/generic/id/57656/title/Homework_makes_the_grade! You can *watch* someone else solve the kinds of problems addressed in this course until doomsday and never learn *anything*. *You will learn best by thinking them through on your own*. On normal homework assignments you are authorized to work in groups of two, but no more. If you have difficulty doing any of the assigned problems, please ask in class, or see the teaching assistant or me during office hours. Whether you ask questions in class or during office hours, please have specific questions. I will want to know whether or not you have really tried to solve the problem and what you have tried. Staying current in the assigned homework will prepare you to work the problems on the quizzes and final exam. Note: in homework assignments you may be asked to “show that” certain results are obtained. If you try to deceive me into thinking that you have done something that you really have not, and I catch it, you will get zero credit for that problem. If I see that several in the class turn in solutions to homework that look the same, a careful evaluation will be done and, if there is solid evidence of unauthorized collusion, this will be treated as a potential **honor code** violation. Note the following:

- Homework papers should use the same notation as is used in the book and in lectures.
- Homework must be neat and professional in appearance. Messy homework papers will not be graded. No cross outs of any kind may appear anywhere.
- Use a straightedge to draw all lines and diagrams.
- Use only good quality paper. Paper torn from a spiral notebook may not be used.
- Explain what you are doing at each step. Credit is given mainly for the method, not the answer.
- Put a box around your final answer to help the grader.
- Write on only the front side of each sheet of paper on all homework papers.
- Staple pages together; “dog-ears” and paperclips will not be accepted.
- Print your name at the upper right corner of the first sheet of paper.
- Only conceptual collaboration is allowed. This means that you may discuss problems with other students. However, all substantive work — such as calculations, derivations, and all written work — must be your own.
- Very similar homework solutions will be viewed as plagiarism and could be submitted as Honor Code violations.
- Use of solutions from prior semesters or any other source (such as solution manuals and web resources) is definitely not allowed and will be treated as a breach of the Honor Code. Students are reminded that they are preparing for a profession (engineering) which has standards for ethical behavior. These standards will be applied toward all class activities and assignments. The Code of Ethics for Engineers is maintained by the American Association of Engineering Societies. See http://www.aaes.org/CodesofEthics.asp.
- Late work will not be accepted unless you have a bona fide excuse (illness certified by doctor’s note, death in immediate family). Excuses will not be granted for travel to conferences, weddings, or whatever. If you must miss class because of any of these things, plan ahead and turn in the work before you leave town.

**Grades**: Do not expect grades to be curved. Moreover, I do not make any use whatsoever of the class average in calculating grades. My expectations for the student are independent of such things. Although *D*‘s and *F*‘s are uncommon, they are not unheard of.

**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; however, if that quiz grade is a zero caused by a no-show, you may not replace it. The project 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.

Flutter projects must be turned in no later than the last day of class, and the structural dynamics/static aeroelasticity project is submitted in three phases, the last of which is turned in on the last day of class. A grade of *C* on the project means a substandard project that fails to meet the stated requirements in some substantial way; a *B* would mean a good project that meets the stated requirements; and an *A* would mean a project that substantially exceeds the stated requirements. On either project you may validate your code by comparing results with those of others, but *you must do all your work independently*. If there is evidence of unauthorized collusion, this will be treated as a potential **honor code** violation and reported to the Dean of Students.

Any individual who asks me to make special provision for him to earn extra credit that is not available for the whole class is asking me to violate the **honor code**. Do not ask.

**Course Objectives 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, assignments and quizzes

Links to videos of interest

Aeroelastic Phenomena and Related Research – Part 1:

Aeroelastic Phenomena and Related Research – Part 2:

Errata for the first printing of the first edition of the Hodges Pierce textbook (all these errors are corrected in the second printing of the first edition)

Errata for the second printing of the first edition of the Hodges Pierce textbook (all these errors are corrected in the third printing of the first edition)

Errata for the third printing of the first edition of the Hodges Pierce textbook (all these errors are corrected in the fourth printing of the first edition)

Errata for the first printing of the second edition of the Hodges Pierce textbook (all these errors are corrected in the second printing of the second edition)

Errata for the second printing of the second edition of the Hodges Pierce textbook (all these errors are corrected in the third printing of the second edition)

Errata for the third printing of the second edition of the Hodges Pierce textbook (all these errors are corrected in the fourth printing of the second edition)

Errata for the fourth printing of the second edition of the Hodges Pierce textbook (all these errors are corrected in the present printing of the second edition)

Errata for the fifth printing of the second edition of the Hodges Pierce textbook (these errors are to be corrected in the event there is another printing of the book)

Instructions for Flutter Project

Instructions for Static Aeroelasticity Project

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Updated 9/10/2018