Level of Education
5 years of post-secondary education
Training Structure
College of Sciences
Description
This 42-hour course is divided into two identical parts that run concurrently. The first part focuses on the study of vibration problems in discrete media and in 1D continuous media (strings, beams). The second part focuses on the use of variational formulations to reformulate the problems studied in L3 into RDM and 3D elasticity. This approach allows us to propose optimized approximate solutions. This part of the course establishes a connection between RDM, 3D elasticity, and the second-semester course on finite elements.
Objectives
Be able to model dynamic problems involving discrete and continuous media and analyze the resulting solutions. In conjunction with the supplementary component of this course, be able to use effective approximation methods (such as the Ritz method).
Review the third-year courses in RDM and 3D elasticity to better connect them and gain a deeper understanding. Learn how to formulate problems as minimization problems so that they can be solved using finite element software in the second semester.
Mandatory Prerequisites
Have completed a bachelor's degree in mechanical engineering, specifically including a course in MMC and a course in RDM.
Course Outline
The course is divided into two parts that run concurrently:
- Vibrations
- Vibrations of Discrete Systems.
Review of the basic concepts of vibrations. Analysis of a system with two degrees of freedom, with and without damping. Free vibrations. Forced vibrations. Analysis of the resonance phenomenon. Analysis of systems with n degrees of freedom. Analysis of natural modes
- Longitudinal and Transverse Vibrations in Beams.
Free vibrations and forced vibrations. Natural modes.
- Applications of Variational Methods.
- Variational Formulation of the Equations of Tension and Bending in Beams. The Principle of Virtual Powers—Energy Minimization. Applications: Approximation of Solutions, Bounding Moduli
- Variational Formulation of the Equations of 3D Linear Elasticity. The Principle of Virtual Powers—Energy Minimization. Applications: Approximation of Solutions, Bounding Moduli