von Karman Institute Lecture Series and Events

VKI Course on Introduction to Aeroelasticity - Aircraft & Turbomachinery (2.0 ECTS)

Monday 19 February 2024 - Friday 23 February 2024

Introduction to Aeroelasticity

This course serves as an introduction to aeroelasticity providing the theoretical basis and hands-on experience for applications to aircraft and turbomachinery design and R&D projects. Starting with the description of the basic aeroelastic phenomena of interest, the course will familiarize the participants with concepts such as aeroelastic deformation, static divergence, control reversal, flutter and gust loads. Aeroelastic modelling techniques of increasing fidelity will be presented and some of them will be practiced. Current industrial practice in aircraft and turbo machinery design will be presented and future avenues will be discussed. Special emphasis is put on interaction with the participants and on practical exercises.

The lecturers are Professor Greg Dimitriadis of University of Liège and Dr. Sina Stapelfeldt of Imperial College London both adjunct professors at the von Karman Institute for Fluid Dynamics.

Dr. Sina Stapelfeldt, Imperial College London, UK & VKI, Belgium

Dr. Sina Stapelfeldt
Imperial College London, UK & von Karman Institute for Fluid Dynamics, Belgium
Lecture Series Director

Prof. Grigorios Dimitriadis, University of Liège, VKI, Belgium

Prof. Grigorios Dimitriadis
University of Liège, von Karman Institute for Fluid Dynamics, Belgium
Lecture Series Director

Learning outcomes:

At the end of the course the participant will have a basic understanding of  

  1. The most important aeroelastic phenomena, such as static divergence, control reversal and flu
  2. The effect of basic system parameters on the occurrence of these phenomena
  3. Gust load response
  4. Low, medium and high-fidelity aeroelastic modelling techniques
  5. Aeroelastic phenomena in turbomachinery
  6. Current industrial practice

Furthermore, the practical exercises are designed  to train application of aeroelastic techniques to practical problems of interest.


The course pre-requisite is a good understanding of aerodynamics, structural vibrations, and finite element methods. Prior use of CFD, and programming skills including familiarity with Matlab. 

Teaching forms

  • Formal lectures: 10 hours
  • Applications: 7 hours
  • Practical sessions: 10 hours

The course will take place from Monday 19 February until 23 February 2024, from 9:00-14:30 with lunch from 12:30 to 13:30 and coffee break from 10:30-11:00.

The registration will start at 08:30 on Monday 19 November;

Course note

Course notes and slides will be delivered. 


References in the Lecture Notes 

EXAM for VKI Research Master students and 2.0 ECTS transfer for university students.

The evaluation is carried out via an oral examination on the 27th of February.


Tentative Agenda

Lunch and coffee breaks in the mornings and afternoons foreseen.

Monday 19 February 2024

Morning: Introduction - static aeroelasticity (3h) - This session will introduce the subject of aeroelasticity and the need for aeroelastic analysis. It will then present the modelling of a typical aeroelastic wing section using quasi-steady aerodynamics. The resulting equations of motion will be solved under static conditions to demonstrate the phenomena of aeroelastic deformation, static divergence and control reversal.

Afternoon: Dynamic aeroelasticity (3h) - The equations of motion derived earlier will be solved under dynamic conditions. The variation of the natural frequencies and damping ratios of the system with airspeed will be demonstrated and the flutter phenomenon will be defined. Finally, the concept of the binary flutter mechanism will be introduced and stability criteria will be presented.

Tuesday 20 February 2024

Practical session: calculate flutter speed of a typical aeroelastic session in Matlab (3h) - The students will develop a Matlab code to calculate the flutter speed of the typical aeroelastic session presented on Day 1. Different stability criteria and numerical procedures will be used.

Unsteady aerodynamics and gusts (4h) - Fully unsteady aerodynamic modelling will be introduced in this session. The Wagner and Theodorsen functions will be introduced and their relationship will be detailed and the effect of fully unsteady aerodynamic modelling on flutter predictions will be discussed. Finally, the problem of a wing flying through an atmospheric gust will be analysed and the Küssner and Sears functions will be introduced. 

Wednesday 21 February 2024

Practical session: Calculate gust load response of a typical aeroelastic function in Matlab (3h) - The students will develop a Matlab code to simulate the passage of the typical aeroelastic section through a sharp-edged gust in the time domain. 

Applications: Aircraft (3h) - This session will be present the standard aeroelastic modelling approaches used in the aircraft industry. The discussion will focus on the combination of a modal model for the structure and the Doublet Lattice Method for the aerodynamics. The solution of the resulting equations of motion will be introduced and examples of aeroelastic analyses of representative aircraft models will be presented.

Thursday 22 February 2024

Applications: High fidelity fluid-structure interaction (2h) - This session will present an introduction into high fidelity modelling of fluid-structure interaction with the help of finite element methods and computational fluid dynamics. Different coupling strengths will be discussed and examples will be given to demonstrate how high fidelity models can be employed in research and industry.

Practical session: Calculation of aerodynamic damping (2h) - The students will work through the work flow for calculating aerodynamic damping of a compressor blade using high fidelity methods. In this first part of the session, the vibration mode shapes will be calculated using finite element methods.

Friday 23 February 2024

Applications: Aeroelasticity simulations of turbomachines  (2h) - This session will introduce structural vibration modes of bladed disks and give an overview of aeroelastic phenomena in turbomachinery, including forced response, stall flutter and non-synchronous vibration.

Practical session: Calculation of aerodynamic damping (2h) - The students will work through the work flow for calculating aerodynamic damping of a compressor blade using high fidelity methods. In this second part of the session, a coupled fluid-structure analysis will be performed and post-processed to calculate aerodynamic damping.

Eligibility Criteria

The citizens of the following countries are eligible to attend the von Karman Institute Lecture Series: check our eligibility criteria here

VKI reserves the right to request a clearance check with Belgian authorities.

The participants will have to present their ID card (for EU citizens) or passport (for other citizens) the first day of the lecture series.

Fee and Registration

While online participation is possible, on-site presence is encouraged - esp. for days 4 and 5 - to get the most from the exercises and interaction with the lecturers and the other course participants. A discount of 10% is applied for an online participation.

Deadline Early Bird Registration: 19 December 2023

Deadline to register: 5 February 2024 for an on-site participation / 12 February 2024 for an online participation

The price includes the course material, lunches and coffee breaks.

Price for citizens of NATO countries (ON-SITE PARTICIPATION)

  Early registration Late registration
Undergraduate students 221 245
PhD students  605 672
Staff from recognized universities / research center 958 1064
Staff from commercial organizations 1210 1344


Price for citizens of other countries (ON-SITE PARTICIPATION)

  Early registration Late registration
Undergraduate students 315 350
PhD students  864 960
Staff from recognized universities / research center 1368 1520
Staff from commercial organizations 1728 1920


Information for PhD candidates and undergraduate students: To obtain the reduced price, the applicant must provide a recommendation letter from his or her professor; if not, the request will not be taken into consideration.

Special reduction

Rebates can be given for group subscriptions along the following scheme :

- 5 persons of the same organization -2%
- 10 persons of the same organization -5%
- 20 persons of the same organization -10%



On-Site  / Online

von Karman Institute for Fluid Dynamics

Waterloosesteenweg 72

B-1640 Sint-Genesius-Rode (near Brussels)

Parking and Safety Information

Parking places are available on the premises, just before the security fence.

To enter, please ring the bell at the fence.


Location : von Karman Institute for Fluid Dynamics

Waterloosesteenweg 72