Structural Dynamics and Aeroelasticity: Course Syllabus

Manav Bhatia∗

Instructor

Name Dr. Manav BhatiaAssistant ProfessorDepartment of Aerospace EngineeringMississippi State University

Office Walker Engineering Bldg., Rm. 318 CPhone (662) 325-7294Email bhatia@ae.msstate.edu

Course Description

Aeroelasticity studies the interaction of aerodynamics and structural motion. With the flight vehicles con-tinuing to push performance boundaries with higher flight speeds and lighter (and more flexible) structures,aeroelasticity has become a major consideration in their design.

This course will cover the essential elements of structural dynamics and extend those concepts to aeroe-lasticity. This will be followed by the study of static aeroelastic phenomenon, such as divergence, controlsurface reversal, etc. The dynamic aeroelastic phenomenon studied will include both flutter instability andgust response. The students will learn about solution methods in the frequency-domain and the time-domain.

Method of Instruction

Course will comprise of lectures delivered face-to-face in class-room.

Textbooks and Course Materials

Course Textbook

Wright, J. R. and Cooper, J. E., Introduction to Aircraft Aeroelasticity and Loads, 2007, John Wiley & SonsLtd., England.

Additional supporting material will be provided as hand-outs, or in electronic form.

Useful References: Structural Dynamics

• Meirovitch, L., Elements of Vibration Analysis, McGraw-Hill, 1975.

Useful References: Aeroelasticity

• Bisplinghoff, R. L., Holt A., and Robert L. H., Aeroelasticity, Dover Publications, 2013.

• Bisplinghoff, R. L., and Holt A., Principles of Aeroelasticity, Dover Publications, 2013.

∗Assistant Professor, Department of Aerospace Engineering, Mississippi State University, email: bhatia@ae.msstate.edu

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• Fung, Y. C., An Introduction to The Theory of Aeroelasticity, Dover Publications, 2002.

• Hodges, D. H., and G. A. P., Introduction to Structural Dynamics and Aeroelasticity, 2nd ed., Cam-bridge University Press, 2011.

• Dowell, E. H., A Modern Course in Aeroelasticity, 5th ed., Springer, 2015.

Prerequisites

• Vibrations (EM 3413) or equivalent

• Programming experience in Matlab or any other language of student’s choice

Course Outline

The course will cover the following topics:

1. Vibration of single and multiple degree-of-freedom systems (2)

2. Vibration of Continuous systems (4)

(a) Natural modes and orthogonality

(b) Response by modal analysis

(c) Kinetic and potential energy

3. Variational Principles for solution of dynamic systems (3)

4. Lagrange’s Equation and Rayleigh-Ritz method (5)

(a) Hamilton’s principle

(b) Generalized coordinates

(c) Conservative systems

(d) Non-conservative systems

5. Free and forced response (3)

6. Topics in Random vibration (5)

(a) Probability density functions and Autocorrelation functions

(b) Power Spectral density functions

(c) Response of systems to random excitations

7. Overview of unsteady potential flow theory (3)

(a) Frequency-domain sectional aerodynamics

(b) Time-domain sectional aerodynamics

8. Static Aeroelasticity (5)

(a) Divergence

(b) Control reversal

(c) Steady-state solution

9. Dynamic Aeroelasticity: Flutter (5)

(a) Concept of frequency-domain, Laplace-domain and time-domain solvers

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(b) V g−method

(c) pk−method

10. Dynamic Aeroelasticity: Discrete Gust Response (3)

11. Dynamic Aeroelasticity: Continuous Gust Response (3)

12. Frequency-domain and Time-domain solution methods (4)

(a) Frequency-domain to time-domain conversion

(b) State-space flutter solution

Method of Evaluation

Assignments (Weekly) 70%Final Project 30%

The graduate students will be given one additional problem per assignment/project. The problem willbe of a higher difficulty level and will count towards the final score on each assignment/project. Theundergraduate students will NOT be required to solve these problems.

Grading

90%-100% A80%- 89% B70%- 79% C60%- 69% D<60% F

Academic Honor Code

Cheating will not be tolerated in this course and will be dealt with according to Mississippi State Universitypolicy. Students are expected to adhere to and uphold the standards of the official honor code of theUniversity: As a Mississippi State University student, I will conduct myself with honor and integrity at alltimes. I will not lie, cheat, or steal, nor will I accept the actions of those who do.

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