Fundamentals of Engineering Structural Dynamics with Python

Leverage fundamental structural dynamics to build your own flexible numerical solutions in Python

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What you'll learn

You’ll learn what separates a static analysis from a dynamic analysis and the key role of inertia
You’ll learn how to model the influence of harmonic loading and how to characterise the transient and steady-state responses
You’ll learn how to model dynamic behaviour using spring-mass-damper models and how to simulate free vibration behaviour
You’ll learn how to use Python to implement the Piecewise Exact Method to model any form of general dynamic loading


Description

This course has two simple objectives:

  1. To help you build a solid understanding of the core concepts in structural dynamics
  2. To equip you with some practical tools you can deploy to analyse real world dynamic structural behaviour

Structural Dynamics is a topic that often intimidates students and practicing engineers. This can be a big problem because not having a good grounding in dynamics, means you can’t confidently simulate, understand and ultimately design for dynamic behaviour. From bridges, to skyscrapers, as engineers, we need to be confident modelling the impact of dynamic loads on our structures. If you’ve tended to shy away from dynamics or found it confusing and intimidating, this course is for you.

We’ll make use of Python throughout the course, but more so towards the second half. This is a hands on, learn by doing course – so there are no dry Python-only lectures, if you’re not familiar with Python – no problem, you’re going to learn what you need as we go…the same way most people learn to programme! This isn’t a ‘Learn Python’ course but you will learn the Python you need, along the way.

Section 1 – Statics versus Dynamics

In section one, we’ll get your coding environment set up. We’ll be using Jupyter Notebooks. These are a hugely popular development environment used throughout science and engineering. This will allow us to get up and running with Python quickly.

After some initial housekeeping we’ll start to discuss the idea of statics versus dynamics and just what makes for a dynamic problem. This will lead us into a brief discussion of inertia. After completing this section you’ll know what differentiates a dynamic problem from a static one and when a dynamic analysis is called for.

Section 2 – Free Vibration of Single Degree of Freedom Systems

In this section we’re going to lay a lot of the groundwork and tackle much of the core theory in structural dynamics. We start by exploring lumped mass analysis and introduce the spring mass damper model. You can think of the spring mass damper model as a fundamental tool used to simulate dynamic behaviour.

We’ll spend the rest of this section examining the characteristics of the spring mass damper model and it’s free vibration behaviour. We’ll cover core concepts along the way such as natural frequency, damping regimes and the logarithmic decrement. We’ll finish out the section with some numerical worked examples and take our first dive into using Jupyter Notebooks.

Section 3 – Harmonic Excitation

This section it about understanding what happens when we introduce an external dynamic force to the system. In particular we’re going to focus on harmonic excitation. We’ll discuss why harmonic excitation is such a key phenomenon to understand and its broader relevance in dynamic analysis.

We’ll develop our understanding of transient and steady-state behaviour. We’ll then go on to characterise the steady-state behaviour and introduce the ideas of dynamic magnification factor and resonance. We’ll finish out this section with a pretty in-depth worked example that will demonstrate exactly how to practically implement everything you’ve learned in the course so far. Again, we’ll be doing this using Jupyter notebooks so you’ll get more exposure to implementing what you’ve learned in Python.

Section 4 – General Dynamic Loading

At this point we’re going to really focus in on giving you some tools to actually perform practical real-world dynamic analyses. We’ll start of by motivating our study of general dynamic loading with a brief case study discussion of human-induced vibration on the Clifton Suspension Bridge in Bristol. This case study highlights the need to have a more versatile dynamic analysis technique in your toolbox

That technique is the Piecewise Exact numerical solution method. This is a hugely versatile numerical solution technique that will equip you with the ability to go beyond harmonic excitation and simulate the influence of any time varying force. We’ll develop the concept, then implement an algorithm in a Jupyter Notebook. The power and versatility of studying structural dynamics in a coding environment will be very apparent in this section. We’ll conclude this section by exploring some of the practical considerations when implementing this and any numerical solution technique.

Who this course is for

  • Undergraduate engineering students who want to get up to speed with structural dynamics
  • Students who’ve studied structural dynamics but got lost along the way
  • Working engineers who are a little rustier than they’d like to admit on dynamics
  • Engineers and students who want to see how they can leverage Python in their work
  • Engineers and students who want a practical technique to analyse realistic dynamic loads


Course preview

Lecture #1: Introduction and course overview

Lecture #5: Introducing inertia

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Course content

Statics versus Dynamics

Fundamentals of Structural Dynamics | DegreeTutors.com - 1
Introduction and course overview (Preview)
(05:11)
Fundamentals of Structural Dynamics | DegreeTutors.com - 2
Our approach to Python (Preview)
(02:05)
Fundamentals of Structural Dynamics | DegreeTutors.com - 3
Getting started with Jupyter Notebooks
(12:10)
Fundamentals of Structural Dynamics | DegreeTutors.com - 4
Static versus dynamic analysis (Preview)
(08:26)
Fundamentals of Structural Dynamics | DegreeTutors.com - 5
Introducing inertia (Preview)
(12:38)
Fundamentals of Structural Dynamics | DegreeTutors.com - 6
Dynamic response and inertia
(13:26)

Free Vibration of Single Degree of Freedom Systems

Fundamentals of Structural Dynamics | DegreeTutors.com - 7
Section overview
(00:54)
Fundamentals of Structural Dynamics | DegreeTutors.com - 8
Lumped mass analysis
(14:44)
Fundamentals of Structural Dynamics | DegreeTutors.com - 9
The spring-mass-damper model
(09:15)
Fundamentals of Structural Dynamics | DegreeTutors.com - 10
The equation of motion
(10:29)
Fundamentals of Structural Dynamics | DegreeTutors.com - 11
Undamped free vibration
(08:53)
Fundamentals of Structural Dynamics | DegreeTutors.com - 12
Natural frequency
(04:39)
Fundamentals of Structural Dynamics | DegreeTutors.com - 13
Damped free vibration
(05:50)
Fundamentals of Structural Dynamics | DegreeTutors.com - 14
Critically damped and over-damped systems
(06:38)
Fundamentals of Structural Dynamics | DegreeTutors.com - 15
Under-damped systems
(07:16)
Fundamentals of Structural Dynamics | DegreeTutors.com - 16
Damped natural frequency
(05:36)
Fundamentals of Structural Dynamics | DegreeTutors.com - 17
Logarithmic decrement
(11:30)
Fundamentals of Structural Dynamics | DegreeTutors.com - 18
Worked Example #1
(24:03)
Fundamentals of Structural Dynamics | DegreeTutors.com - 19
Worked Example #2
(42:07)

Harmonic Excitation

Fundamentals of Structural Dynamics | DegreeTutors.com - 20
Section overview
(00:55)
Fundamentals of Structural Dynamics | DegreeTutors.com - 21
Harmonic forcing
(09:02)
Fundamentals of Structural Dynamics | DegreeTutors.com - 22
Solving the equation of motion
(14:14)
Fundamentals of Structural Dynamics | DegreeTutors.com - 23
Characterising the steady-state response
(13:49)
Fundamentals of Structural Dynamics | DegreeTutors.com - 24
The dynamic magnification factor & resonance
(27:58)
Fundamentals of Structural Dynamics | DegreeTutors.com - 25A
Worked Example #3 – Part A
(09:06)
Fundamentals of Structural Dynamics | DegreeTutors.com - 25B
Worked Example #3 – Part B
(19:17)
Fundamentals of Structural Dynamics | DegreeTutors.com - 25C
Worked Example #3 – Part C
(20:14)

General Dynamic Loading

Fundamentals of Structural Dynamics | DegreeTutors.com - 26
Section overview
(01:03)
Fundamentals of Structural Dynamics | DegreeTutors.com - 27
General dynamic loading and feedback
(11:48)
Fundamentals of Structural Dynamics | DegreeTutors.com - 28
The Piecewise Exact Method – concept
(07:56)
Fundamentals of Structural Dynamics | DegreeTutors.com - 29
The Piecewise Exact Method – development
(12:48)
Fundamentals of Structural Dynamics | DegreeTutors.com - 30
Implementing the Piecewise Exact Method
(29:13)
Fundamentals of Structural Dynamics | DegreeTutors.com - 31
Force segmentation
(25:47)
Fundamentals of Structural Dynamics | DegreeTutors.com - 32
Time discretisation
(14:12)
Fundamentals of Structural Dynamics | DegreeTutors.com - 33
Course wrap up
(00:50)


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