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Developments of structural dynamics
  • Level Professional
  • Duration 10 hours
  • Course by ISAE-SUPAERO
  • Offered by

About

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. 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 shocks theory and general dynamic representation of structures and foundations of the dynamic tests and certification. In fact, this course is a perspective on the double vision of any dynamic structure, with the continuous point of view and a digital model in perspective. At the end of this course, the physicist, the mechanical engineer, the specialist in control will have a general overview of the dynamic representation and implicit solution applicable in structural analysis and control of general dynamic systems. In a certain way, it is founded on the famous discussions between Albert Einstein and Niels Bohr. Recommendation: we suggest having a look, at the course "Foundation of structural dynamics: from static to discrete dynamics". This course proposes an original point of view of the foundations of dynamics. And could highlight the present course.

Modules

Inroduction

    • 2 Videos
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2 Videos

  • Welcome to the course
  • General notation

Lagrange's parameters

    • 2 Videos
    • 1 Readings
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2 Videos

  • Lagrangian equation
  • Lagrangian potential

1 Readings

  • Few words before starting

Exercise: Articulated rotor

    • 1 Readings
    • 1 Plugin
    • 1 Assignment
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1 Assignment

  • Few questions about articulated rotor

1 Readings

  • Exercise statement

Complete Lagrange's equation

    • 3 Videos
    • 1 Readings
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3 Videos

  • Lagrange's complete equation
  • Lagrange's selftraining - The problem
  • Lagrange's exercise - The solution

1 Readings

  • Self training

Linearity - The limits of this world

    • 1 Videos
    • 1 Readings
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1 Videos

  • Linearity in dynamics

1 Readings

  • Linearity, what does it means

Assessment

    • 1 Assignment
Show info about module content

1 Assignment

  • Quiz Week 2

Free matrix dynamics

    • 5 Videos
    • 1 Readings
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5 Videos

  • Matrix equation
  • Eigenshapes - Part 1
  • Eigenshapes - Part 2
  • Eigenshapes - Part 3
  • Matrix diagonalisation will now occur!

1 Readings

  • Reading

Training on matrix equations

    • 2 Videos
    • 2 Readings
    • 1 Discussion
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1 Discussions

  • Discussion on the exercise

2 Videos

  • Statement of the exercise
  • Solution: Miraculous generation of the equations

2 Readings

  • Before you start
  • Synthesis

Application: Winching

    • 1 Readings
    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Quiz on winching

1 Discussions

  • The magic of dynamics

1 Readings

  • Winching

Evaluation

    • 1 Videos
    • 1 Assignment
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1 Assignment

  • Evaluation on Matrix equations

1 Videos

  • Statement of the quiz

The digital approach

    • 3 Videos
    • 1 Readings
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3 Videos

  • Static introduction
  • Deep exploration of spline's formula
  • Generic solution of bended beam

1 Readings

  • Summary

Boundary conditions and free solution

    • 4 Videos
    • 1 Readings
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4 Videos

  • Mechanical boundary condition - Part 1
  • Mechanical boundary condition - Part 2
  • Mechanical boundary condition - Part 3
  • Mechanical boundary condition - Part 4

1 Readings

  • Summary

Application: Effective modal masses

    • 1 Readings
    • 1 Discussion
    • 1 Assignment
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1 Assignment

  • Quiz about effective modal masses

1 Discussions

  • The power of eigenshapes

1 Readings

  • Effective modal masses - Additionnal perspectives

Vibration nodes and bellies/Excited solution

    • 1 Videos
    • 1 Readings
    • 1 Plugin
    • 1 Assignment
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1 Assignment

  • Quiz about vibration nodes and bellies

1 Videos

  • Vibration nodes and bellies

1 Readings

  • Experiment lab

Genaral assessment

    • 1 Readings
    • 2 Assignment
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2 Assignment

  • Part 1: Digital system
  • Part 2: Continuous system and critical analogy

1 Readings

  • Digital and continuous translation system

Auto Summary

Immerse yourself in the "Developments of Structural Dynamics" course, tailored for science and engineering professionals. Led by Coursera, this comprehensive 600-hour course delves into dynamic structural analysis using continuous elements versus discrete models. Emphasizing Lagrange’s equation, matrix representation, and Gaussian modes, it is ideal for physicists, mechanical engineers, and control specialists. Enhance your understanding of dynamic systems with practical insights into vibration, shocks theory, and dynamic testing. Available through Starter and Professional subscriptions, this course offers a profound perspective rooted in the debates of Einstein and Bohr.

Yves Gourinat
Instructor

Yves Gourinat