This course is devoted to the dynamic implementation of continuous structural elements vs discrete models. The matrix representation and implicit solution of Lagrange’s equation are at the heart of this approach, in the framework of conservative structural systems, with Gaussian modes.
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Developments of structural dynamics
ISAE-SUPAEROÀ propos de ce cours
Dates limites flexibles
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Certificat partageable
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100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Niveau intermédiaire
Knowledge of point physics, matrix mathematics,solid mechanics and statics of beams will be particularly helpful.
Approx. 10 heures pour terminer
Anglais
Sous-titres : Anglais
Ce que vous allez apprendre
To implement a matrix approach of dynamics system.
To understand the deep signification of the Lagrange representation.
To be able to make the link between a digital and a continuous dynamic system.
Dates limites flexibles
Réinitialisez les dates limites selon votre disponibilité.
Certificat partageable
Obtenez un Certificat lorsque vous terminez
100 % en ligne
Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Niveau intermédiaire
Knowledge of point physics, matrix mathematics,solid mechanics and statics of beams will be particularly helpful.
Approx. 10 heures pour terminer
Anglais
Sous-titres : Anglais
Offert par
ISAE-SUPAERO
ISAE-SUPAERO, world leader in aerospace engineering higher education, has trained over 21,000 highly skilled engineers since its creation in 1909. We have been educating students to have the most advanced scientific and engineering skills, helping the aeronautics and space industry to anticipate and adapt to the latest scientific, economic and social changes. We welcome the best students from all over the world and educate them to be future responsible leaders driving the development of our society and contributing to technological innovation in aeronautics and space. Located in Toulouse, France, we benefit from a unique ecosystem, both at the heart of the European capital for aeronautics and space and of a thriving aerospace higher education and research campus.
Programme de cours : ce que vous apprendrez dans ce cours
2 heures pour terminer
Analytical dynamics
We will discover the power of Lagrange formalism able to generate the equation of any discrete dynamic system. This seems miraculous because, from energies, we directly extract the complete dynamic equations.
2 heures pour terminer
4 vidéos (Total 11 min), 2 lectures, 1 quiz
1 heure pour terminer
Linear structures
Linearity is an important domain. Not only because it corresponds to powerfull mathematic tools but also because it's a nominal way to move for a structure. In this topic, we master the modeling of any digital linear system.
1 heure pour terminer
4 vidéos (Total 16 min), 2 lectures, 1 quiz
3 heures pour terminer
Discrete eigenshapes
We solve the digital dynamic system by Gaussian diagonalization, thus we discover the concept of natural shapes (or eigenshapes), fundamental for the dynamic behavior of any structure. This opens the world towards resonances and implicit analysis. In fact, the modes represent the actual dynamic DNA of the structure.
3 heures pour terminer
8 vidéos (Total 36 min), 4 lectures, 2 quiz
3 heures pour terminer
Dynamics of beam
Real structures are made with continuous beams and shells. Beams are the ideal prototype for the demonstration of continuous modes showing clearly that there is no fundamental difference between discrete and continuous dynamic shapes. We solve the essential problem of bended dynamic beam representing for instance a bridge, a wing, a javelin in flight, etc.
3 heures pour terminer
8 vidéos (Total 44 min), 4 lectures, 2 quiz
1 heure pour terminer
General assessment
1 heure pour terminer
1 lecture
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