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ISAE-SUPAERO via Coursera |
Go to Course: https://www.coursera.org/learn/developments-of-structural-dynamics
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.
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.
Linear structuresLinearity 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.
Discrete eigenshapesWe 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.
Dynamics of beamReal 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.
General assessmentThis 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. The prototype of the continuous element being the prismatic beam - as an illustration, but with general value - and the implicit model/solution leads to the major place of natural eigenshapes in vibration and sh