Course Syllabus

Instructor Information

Prof. Canfield, 214 Randolph Hall, 231-5981,
  • Class hours: 11:00AM–12:15PM,TR, McBryde 204
  • Office hours: 3:00PM–4:00PM MWF, RANDolph 214 (or by appointment)

Catalog Description

Aeroelastic phenomena including flutter, divergence, control surface effectiveness, and lift redistribution; and introduction to traditional and modern methods of analysis and remedies for aeroelastic problems of flight vehicles.  Pre: AOE 5034 (ESM 5304), AOE 5104, AOE 5214, or equivalent. (3H, 3C)


AOE 5034 (ESM 5304), Mechanical and Structural Vibrations, provides the necessary background on structural dynamics. AOE 5104, Advanced Aero and Hydrodynamics, provides basics of aerodynamic forces. Familiarity with applying these basic concepts to aircraft comes from AOE 5214, Aircraft Dynamics and Control. Undergraduate equivalents to latter two courses will be accepted.

Textbook & Software

Required Course Textbook

Introduction to Structural Dynamics and Aeroelasticity, Hodges & Pierce, 2nd Ed., Cambridge, 2011

Supplemental References

Aeroelasticity, Bisplinghoff, Ashley & Halfman, 1996 (recommended)

A Modern Course in Aeroelasticity, Dowell (editor), 2004 (recommended)

Computer Software

Most assignments require numerical computation in a computer programming language or tool of the student's choice. Some assignments will call for use of Zona Technology's ZAERO aeroelasticity program. It requires natural modes of vibration from Nastran as input. Zona offers ASTROS as a publicly accessible alternative for computing vibration modes. AOE has a limited site license for ZAERO; a  demonstration version is freely available for academic use.

Course Objectives

Having successfully completed this course, a student will be able to:
  • Explain structural concepts such as elastic stiffness, inertia, influence coefficients, elastic axis, and shear center.
  • Describe structural dynamics of wings, including bending and torsion modes of vibration and their associated natural frequencies.
  • Describe aerodynamic concepts such as a typical section airfoil, aerodynamic center, and lift and moment coefficients.
  • Apply aeroelastic concepts of divergence, flutter, lift and roll effectiveness, aileron reversal, and mode coalescence.
  • Derive static and dynamic aeroelastic equations of motion.
  • Approximate continuous aeroelastic systems using the Rayleigh-Ritz Method.
  • Solve for aeroelastic response.
  • Interpret velocity-damping and velocity-frequency flutter diagrams.
  • Apply k- and p-k flutter methods to solve the parametric aeroelastic eigenvalue problem.
  • Solve flutter problems with a spline between structural and aerodynamic models.
  • Demonstrate ability to formulate, model, and analyze an aeroelastic system.

Course Schedule (Syllabus)

Hour Topic Dowell Hodges (1st ed.) 2nd ed. BAH
1 Introduction & Administration 1 1 1
2 Torsion Theory   (2.2) 2.3.1, 3.2 2-12
3 Euler-Bernoulli Beam Theory   (2.3) 2.3.2, 3.3 2-3, 2-8…11
4 Equivalent Spring Beam Stiffness     8-2
5 Rayleigh-Ritz Method 3.7 (2.4) 3.5.1 3-10
6 Coupled Modes     4-2
7 Typical Section 2.1 (4.2) 4.1, 5.2 8-2
8 Divergence   (3.1.1) 4.1.1 8-3
9 Aileron Reversal   (3.1.4) 4.1.4 8-3
10 Flexible Aileron Reversal 2.1   8-3
11 Strip Theory 2.2 (3.2) 4.2.1 5-4
12 Torsional Divergence   (3.2.2) 4.2.3 8-3
13 Air Load Distribution   (3.2.3) 4.2.4 8-3
14 Divergence Eigenvalue / Galerkin 2.2 (2.4.2) 3.5.2 8-3
15 Swept Wing Divergence 2.6 (3.2.4) 4.2.6 8-4
16 Roll Reversal 2.3    
17 Roll Effectiveness 2.3    
18 Influence Coefficients 2.4 (4.1) 5.1 5-5
19 Typical Section Equations of Motion 3.2   9-1,2,3
20 SdoF Torsional Flutter   (4.3.1) 5.3.1 9-2
21 Typical Section, Non-Dimensional p. 88 (4.2) 5.2  
22 Two-DoF Flutter 3.3 (4.3.2) 5.3.2 9-2
23 V-g and V-w Diagrams     9-4
24 Quasi-Steady Aerodynamics 3.3   5-6
25 p Method 3.3 (4.4.2) 5.4.2  
26 k and p-k Methods   (4.4.1) 5.4.1 Ex. 9-1
27 Mid-Term Exam on Hours 1–26
28 Quasi-Steady Aerodynamics 3.4 (4.5) 5.5  
29 Quasi-Steady Beam Flutter     9-3
30 Quasi-Steady Aero, Assumed Modes 3.3 (4.5) 5.5 9-4,5
31 Dynamic Aeroelasticity (Plate) 3.2 (4.1) 5.1  
32 ZAERO input and output  
33 Goland Wing     9-3
34 Splining ZAERO Theoretical Man. 6.1  
35 Aerodynamic Influence Coefficients     8-4, 9-11
36 Theodorsen Aerodynamics 4.3 (4.5.1) 5.5.1 5-6, 9-3
37 Theodorsen Aero, Assumed Modes 4.6 (4.6) 5.6 9-5
38 Doublet Lattice Aerodynamics WL–TR–95–3022  
39 Review / Course Critiques  

Administrative dates and information for this class are provided by the Office of the Registrar:

Grading Policy

Class Participation 10%
Homework 25%
 In-Class Test 1 20%
 In-Class Test 2 20%
 Final Project 25%

Tests will be graded on a standard numeric scale. If the mean is below a B, then scaled T-scores* may be used to determine letter grade for the test. 

Grading Scale
 A  >= 93
 A–  >= 90
 B+  >= 87
 B  >= 83
 B–  >= 80
 C+  >= 77
 C  >= 73
 C–  >= 70
 D+  >= 67
 D  >= 63
 D–  >= 60
 F  >= 0

Each homework problem and the final project will be graded on the following letter grade scale. The homework letter grades will be converted to a numeric score, according the the test grading scale, incorporating class participation.

Homework and Project Grades
A Correct Answer and Method
B Correct Method
C Nice Try
D No Clue
F No Attempt

Students are encouraged to discuss homework problems with one another and may compare approach and results, but they are expected to turn in their own, individual work. Do not share computer code. Submit only assignments that are your own work.

The final project grade will be based on a final class presentations and a final written report, equally weighted.

*The article "Testing Memo 6: What kind of Grades Should be Averaged?" at following link explains T-scores.

Honor System

Students shall work independently on tests, exams, and projects and submit only their own work. Students are permitted to discuss homework problems in groups, but they are expected to turn in their own, individual work. Computer programming code may not be shared, copied, or distributed among students before an assignment is due.

Student and instructor behavior in this class is governed by the Virginia Tech Honor Code and its core values:

  • Mutual Trust
  • Intellectual Honesty
  • Honesty and Integrity promote quest for Truth
All assignments submitted shall be considered graded work and shall be completed on an individual basis, unless otherwise stated. While discussing assignments and getting help outside of class is both authorized and encouraged, copying solutions from any source is considered a violation, as is sharing or re-use of an unauthorized (i.e., not provided or authorized by the instructor) computer file in full or in part. Honesty in your academic work will develop into professional integrity. The faculty and students of Virginia Tech will not tolerate academic dishonesty. It is your responsibility to seek clarification if there is a question about how the Honor Code applies to a given assignment.

Attendance and Classroom Behavior

Virginia Tech has a class attendance policy. Class meetings are an integral part of most courses and are the central component of many. Students and faculty are expected to attend class at all regularly scheduled times, except for cancellations announced on a university wide basis by the appropriate authority. When students cannot attend a class, it is their responsibility, as soon as possible, to consult with the course instructor about missed work or tests.

Students are expected to respect one another and the instructors in and outside the classroom. Computers may be used in the classroom only for viewing material for this course or for taking notes. Accessing audio, images, or videos during class may be distracting to other students and is strictly prohibited. Cell phone use is prohibited, except as a student response system.

Policy for Making Up Assignments

Requests to make up for a missed test or assignment must be made by notifying the instructor in advance of the scheduled due date. Requests due to absences shall be documented through the the Dean of Students, who can verify your absence and notify all of your instructors at once. In case of absences for health reasons, Schiffert Health Center medical staff can verify that you have been given medical treatment. For family or personal emergencies, students should consult with Dean of Students Office, who will notify the Associate Dean of Academic Affairs for Engineering. Circumstances out of the student's control, such as illness, a death in the family, or making a presentation at a professional conference, shall normally be considered an excused absence that justifies the request. Circumstances within the student's control are normally considered an unexcused absence for which a make-up request may be denied.

Unscheduled or undocumented requests will be granted or denied at the discretion of the instructor. The make-up test may be an oral exam.

Students may not discuss with other students a test being made up in between the time the student and the class take the test.

Students with Special Needs

Reasonable and appropriate academic accommodations will be made for students who provide documentation of disability and request for such accommodation.


Please inform the instructor and teaching assistant within the first two weeks of class of potential conflicts that may arise due to participation in religious or ethnic holiday events.

Emergency Preparedness

Final Project (Exam)

The final project report will be due on December 13, 2016.

Course Summary:

Date Details Due