Developments of structural dynamics

Developments of structural dynamics

Name: Developments of structural dynamics
Rating: 4.428571428571429 (14 reviews)

Instructor: Yves Gourinat

2,162 already enrolled

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5 modules

Gain insight into a topic and learn the fundamentals.

14 reviews

Intermediate level

Recommended experience

1 week to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

5 modules

Gain insight into a topic and learn the fundamentals.

14 reviews

Intermediate level

Recommended experience

1 week to complete

at 10 hours a week

Flexible schedule

Learn at your own pace

What you'll learn

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.

Skills you'll gain

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Assessments

8 assignments

Taught in English

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There are 5 modules in this course

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.

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.

What's included

4 videos2 readings1 assignment1 plugin

4 videos Total 11 minutes

Welcome to the course 4 minutes
General notation 3 minutes
Lagrangian equation 2 minutes
Lagrangian potential 2 minutes

2 readings Total 35 minutes

Few words before starting 5 minutes
Exercise statement 30 minutes

1 assignment Total 30 minutes

Few questions about articulated rotor 30 minutes

1 plugin Total 15 minutes

Dual articulated rotor (integrated exercise) 15 minutes

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.

What's included

4 videos2 readings1 assignment

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.

What's included

8 videos4 readings2 assignments2 discussion prompts

8 videos Total 36 minutes

Matrix equation 4 minutes
Eigenshapes - Part 1 8 minutes
Eigenshapes - Part 2 4 minutes
Eigenshapes - Part 3 2 minutes
Matrix diagonalisation will now occur! 4 minutes
Statement of the exercise 4 minutes
Solution: Miraculous generation of the equations 6 minutes
Statement of the quiz 4 minutes

4 readings Total 67 minutes

Reading 10 minutes
Before you start 2 minutes
Synthesis 10 minutes
Winching 45 minutes

2 assignments Total 60 minutes

Quiz on winching 30 minutes
Evaluation on Matrix equations 30 minutes

2 discussion prompts Total 20 minutes

Discussion on the exercise 10 minutes
The magic of dynamics 10 minutes

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.

What's included

8 videos4 readings2 assignments1 discussion prompt1 plugin

8 videos Total 44 minutes

Static introduction 5 minutes
Deep exploration of spline's formula 3 minutes
Generic solution of bended beam 9 minutes
Mechanical boundary condition - Part 1 4 minutes
Mechanical boundary condition - Part 2 5 minutes
Mechanical boundary condition - Part 3 5 minutes
Mechanical boundary condition - Part 4 4 minutes
Vibration nodes and bellies 9 minutes

4 readings Total 80 minutes

Summary 10 minutes
Summary 10 minutes
Effective modal masses - Additionnal perspectives 40 minutes
Experiment lab 20 minutes

2 assignments Total 50 minutes

Quiz about effective modal masses 30 minutes
Quiz about vibration nodes and bellies 20 minutes

1 discussion prompt Total 10 minutes

The power of eigenshapes 10 minutes

1 plugin Total 15 minutes

Access to IREAL platform 15 minutes

What's included

1 reading2 assignments

Instructor

Yves Gourinat

ISAE-SUPAERO

3 Courses 7,730 learners

Offered by

ISAE-SUPAERO

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