• Level of study

    BAC +5

  • Component

    Faculty of Science

Description

This 42-hour course is divided into two identical parts that run in parallel. The first part concerns the study of vibration problems in discrete media and in 1D continuous media (string, beams). The second part concerns the use of variational formulations in order to reformulate the problems studied in L3 in RDM and 3D elasticity. We can then propose optimized approximate solutions. This part of the course allows to make a link between RDM, 3D elasticity and the second semester course of finite elements.

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Objectives

Know how to model problems in dynamics concerning discrete media, continuous media and analyze the solutions obtained. In connection with the complementary part of this course, know how to use efficient approximate methods (Ritz method for example).

Review the L3 courses on RDM and 3D elasticity in order to better link and deepen them. Learn to formulate the problems as minimization problems in order to be able to process them with a finite element code in the second semester.

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Necessary pre-requisites

Must have completed a Bachelor's degree in mechanics and in particular a course in MMC and a course in RDM.

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Syllabus

The course is divided into two parts that run in parallel:

 

  1. Vibrations

 

  1. Vibrations of discrete systems.

Reminder of the basic notions of vibration. Study of a system with two degrees of freedom with or without damping. Free vibrations. Forced vibrations. Study of the resonance phenomenon. Study of systems with n degrees of freedom. Study of eigenmodes

 

  1. Longitudinal and transverse vibrations in beams.

Free vibrations and forced vibrations. Normal modes.

  1. Applications of variational methods.

 

  1. Variational writing of the tensile and bending equations of beams. Principle of virtual powers - Energy minimization. Applications: approximation of solutions, framing of modules
  2. Variational writing of 3D linear elasticity equations. Principle of virtual powers - Energy minimization. Applications: approximation of solutions, framing of modules

 

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