42366 - Structural Dynamics and Aeroelasticity

Learning outcomes

Construction and resolution capability of simplified analytical model adopted to describe the dynamic behaviour of continuos three-dimensional structures.
Critical analysis of geometrical and physical parameters effects on the dynamics of mechanical systems.
Construction of simplified analytical models adopted to investigate, in a preliminary way, static and dynamic aeroelastic response of aerospace structures.

Course contents

Part I: Lectures and exercise

1. Engineering scheme of dynamic systems.
2. Dynamic degrees of freedom of continuous and/or discrete structures.
3. Discussion of analytical solutions of one degree of freedom oscillator.
4. The virtual work and the Lagrange theorems applied to describe the equations of motion of elastic systems.
5. Preliminary explanation of the Rayleigh method.
6. Discrete systems with "n" degrees of freedom: equations of motion, characteristic equation. Modal analysis of discrete systems.
7. Continuos systems: string dynamics, membrane dynamics, beam dynamics, plate dynamics.
8. Modal analysis of continuous systems: integral formulation of the eigenvalues problem (assumed functions method).
9. Energetic approaches to dynamic problems: the Rayleigh-Ritz method, the Faedo-Galerkin-Kantorovich method.

Part II: Lectures and exercise

1. Preliminary description of aeroelastic phenomena: static divergence, loads redistribution, static aileron efficiency, buffeting, flutter.
2. Torsional divergence of high aspect ratio unswept wings: closed form solution of the problem.
3. Energetic approaches to the torsional divergence of high aspect ratio unswept wings.
4. Aeroelastic effects on the symmetrical and unsymmetrical lifting distribution for high aspect ratio unswept wings.
5. High aspect ratio swept wings: torsional and flexural combined behaviour.
6. Static aeroelastic stability conditions for high aspect ratio swept wings.
7. Detailed description and physical interpretation of lifting surfaces flutter.
8. Calculation of aerodynamic loads in the case of two dimensional unsteady motion: the delay Wagner function method.
9. The Theodorsen method to determine the flutter condition of a two dimensional rigid wing section: the case of two elastic degrees of freedom.
10. Flutter analysis by means of the assumed functions method: examinations of typical cases valid for traditional aircraft configurations.
11. Numerical flutter analysis: flutter equation obtained assuming as unknown the generalised co-ordinates.
12. Solution of flutter equation by means of numerical methods: the p-k method and the non-linear direct method.

Readings/Bibliography

Dynamics of Structures - R.W. Clough, J. Penzien, Ed. McGraw-Hill, 1975.

Aeroelasticity - R.L. Bisplinghoff, H. Ashley and R.L. Halfman, 1996.

An introduction to the theory of aeroelasticity - Y.C. Fung, 1993.

Assessment methods

During the first examination phase student must resolve two distinct exercises: a structural dynamics problem and a problem of aeroelasticity (static or dynamic).
In the next phase it takes place a discussion of results obtained by the student and some questions about theory (modal analysis and aeroelasticity) will be asked.

Office hours

See the website of Mario Rosario Chiarelli