Structural Dynamics and Aeroelasticity (2nd edition)


The course is an introduction to the Finite Element Method (FEM) and its application to the field of Structural Dynamics. For practical application NASTRAN software environment is recommended. Focus on fluid-structure coupling is made. The fluid forces exerted on the structure for incompressible and compressible flows is also considered. Aeroelastic application in NASTRAN software environment will be given.

Delivered by:
Universidad Politécnica de Madrid

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Beginning with a brief description on the different numerical methods and their application to the field of structural dynamics the course evolved towards the most popular of them, the Finite Element Method (FEM). The simple case of one dimensional structural elements is first approached. Different options to obtain the mass matrix for the structural element are considered.

Next, two dimensional structural elements like plates, shells or membranes are studied. Different methods for the computation of the natural frequencies and normal modes of the vibrating structure will be given and their physical meaning explained. Application to aeronautical structure will be presented.

The second part of the course is dedicated to the field of Aeroelasticity. First, the aerodynamic forces exerted by the fluid on the structure at low, medium and high velocities will be considered.
The coupling of the fluid-structure is finally studied, focusing on the cases of structural stability and structural response.

Duration: 50 hours of study (12 weeks)

Start: 9th October 2023
End: 31st December 2023

Target audience: 

  • Aerospace and Mechanical Engineers or Graduate students working in the areas of structural dynamics and Aeroelasticity.

Learning goals:

  • The participant will get knowledge on the fundamentals of mechanical vibrations and unsteady aerodynamics and their coupling for the aeroelastic problem.
  • The participant will be able to describe, discuss and use finite element models for analysing the structural dynamics of one and two dimensional structures.
  • The participant will be able to explain the key elements and fundamental theories of unsteady aerodynamics.
  • The participant will be able to distinguish and formulate the static and dynamic aeroelastic problems.
    The participant will be able to describe the procedures and background relationships involved in flight tests.


  • Module 0. Vibration: basic concepts
  • Module 1. Structural Dynamics
  • Module 2. Finite Element Analysis, one-dimensional elements
  • Module 3. Finite Element Analysis, two-dimensional elements
  • Module 4. Aerodynamics, basic concepts
  • Module 5. Unsteady Aerodynamics
  • Module 6. Introduction to Aircraft Structural Dynamics and Aeroelasticity
  • Module 7. Static Aeroelasticity
  • Module 8. Dynamic Aeroelasticity
  • Module 9. Aeroelasticity with MSC.Nastran
  • Module 10. Flight Vibration Tests FVTs

Technical requirements:

  • The student must have a laptop with calculation options.

Recommended previous knowledge:

  • Knowledge of static and dynamic structural calculations.
  • Basic aerodynamics knowledge.
Félix Arévalo
Aeronautical Engineer (UPM) and PhD (UPM). Airbus Expert in Structural Dynamics and Aeroelasticity (SD&A) and Designated Certification Specialist (DCS) in Aeroelasticity for the Airbus A400M programme. 25 years of experience in Aeronautical Industry: ITP-Allied Signal and Airbus-DS. Currently Team Leader of the Spain-site Structural Dynamics and Aeroelasticity group.Also, Associate Professor of SD&A in the Technical University of Madrid, responsible of the fluid-structure interaction module of the UPM-ANSYS On-line Master and responsible of the OAD module of the UC3M-Airbus Master. Author of more than 37 papers presented in different journals and congresses. Member of the IFASD (International Forum of Aeroelasticity and Structural Dynamics) International Technical Committee and technical referee in different journals.
Pablo Gracía-Fogeda
Dr. Pablo García-Fogeda got his PhD. From Arizona State University and is currently full professor at the Universidad Politécnica de Madrid in the area of Aerospace Engineering. He has more than 30 year of experience teaching graduate and undergraduate courses on Structural Dynamics, Aeroelasticity and Vibroacoustics. He is the author of the books Introducción a las Vibraciones and Introducción a las Aeroelasticdad by Ed. Garceta. Prof García-Fogeda has published over 50 research papers on the subjects of Structural Dynamics, Aeroelasticity and Unsteady Aerodynamics.
Marcos Chimeno
Aerospace engineer by Universidad Politécnica de Madrid in 2016 and PhD in Aerospace Engineering by Universidad Politécnica de Madrid on 2014, his main research area is structural dynamics with special interest in fluid-structure interaction, i.e. vibro-acoustics. Regarding this area of research, he has taken part in several research projects as public funded projects: several European projects, ESA initiatives programmes or National Plan for Scientific Research funded programmes. In addition to these projects that were focused on structural and vibro-acoustic analysis, he has also developed several projects in collaboration with space industry, with special focus on the numerical simulation and experimental testing of space components and elements. The research developed along these projects has led to the publication of 11 JCR journal papers and over 30 conference papers, some of them as invited paper.

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