Fundamentals of Engineering Structural Dynamics with Python

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 practising 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.