# MEng Aerospace Engineering with Industrial Experience / Course details

Year of entry: 2024

## Course unit details:Vibrations & Aeroelasticity (Aerospace)

Unit code AERO31441 10 Level 3 Semester 1 No

### Overview

The aims of the course are the impartation of understanding and problem-solving skills in a range of vibration and aeroelastic problems. The vibration problems include discrete and continuous systems, which are solved using matrix algebra and partial differential equations, respectively. The aeroelastic problems deal with phenomena involving structural instabilities such as divergence and flutter, in gas, wind and steam turbine blades, aircraft wings, buildings, bridges and surface vehicles due to the interaction of aerodynamic, elastic and inertia forces.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Dynamics MECH20442 Pre-Requisite Compulsory

### Aims

The aims of the course are the impartation of understanding and problem-solving skills in a range of vibration and aeroelastic problems. The vibration problems include discrete and continuous systems, which are solved using matrix algebra and partial differential equations, respectively. The aeroelastic problems deal with phenomena involving structural instabilities such as divergence and flutter, in gas, wind and steam turbine blades, aircraft wings, buildings, bridges and surface vehicles due to the interaction of aerodynamic, elastic and inertia forces.

### Syllabus

The course consists of two broad divisions, namely: Vibrations Theory and Aeroelasticity. The course syllabus is as follows;

1. Vibrations of Multiple Degrees of Freedom Discrete Systems

Definitions and examples of degrees of freedom; discretisation using load-sharing approach;

Derivation of equations of motion using: Newton's law, Lagrange's equation, stiffness & flexibility influence coefficients;

Eigenvalue problem: natural frequencies and mode shapes;

Orthogonality of modes, transformation from physical to modal space/co-ordinates;

Proportional and non-proportional damping.

2. Vibrations of One-dimensional Continuous Systems

Wave theory : derivations and solutions of wave equations for transverse vibrations of strings; longitudinal and torsional vibrations of rods and shafts; exact frequency equations.

3. Vibrations of Self-Excited Non-Aerodynamic Systems

Dynamic stability of a system: Poles and zeros method; Routh-Hurwitz stability criteria;

Non-aerodynamic self-excited systems: Shimmy of wheels.

4. Static Aeroelasticity of Blades and Wings

Effects of aeroelastic flexibility: stiffness and deflection changes;

Divergence and static stability, airfoil twist angle amplification, aeroelastic feedback.

5. Dynamic Aeroelasticity of Blades and Wings

Vortex shedding from single cylinder;

Unsteady aerodynamics, representation of relationship between forces and motion;

Forced harmonic motion with unsteady aerodynamics;

Flutter analysis.

Method Weight
Written exam 70%
Report 30%

### Feedback methods

Written feedback on laboratory report

### Study hours

Scheduled activity hours
Assessment written exam 2
Lectures 24
Practical classes & workshops 3
Independent study hours
Independent study 71

### Teaching staff

Staff member Role
Tunde Oyadiji Unit coordinator

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