1. Introduction and course overview
Welcome and preliminaries
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Welcome to the course! In this short lecture, I’ll give you an overview of the course and help you get a better understanding of what you’ll have achieved when you complete the course.

This course is for anyone who wants to understand multi-degree of freedom structural dynamics. The course is built around the theme of seismic analysis and determining the response of structures to earthquake-induced ground motion. In reality, that’s just one form of excitation and when you complete the course you’ll be able to handle ground motion as well as any kind of directly applied dynamic loads such as wind loading or blast pressure waves for example.

As you move through the course, you’ll be developing your understanding of the theory - but at each stage, you’ll implement what you learn using Python. This way you get to see the application of what you’re learning at every stage - this really helps bring the theory to life and is a great way to learn about structural dynamics.

The course culminates in you developing a code for analysing the response of multi-story structures to realistic ground motion. The final code will be capable of handling anything from a 2 to 200 storey shear building. More important than the code itself, is the fact that you’ll understand how and why every line of it works - meaning you’ll have no problem adapting it or further developing or customising it for your own use beyond this course.

Section 2 - Introduction to Ground Motion Modelling

The next section starts by covering some of the fundamental topics in the context of SDoF systems. We’ll look at developing analytical solutions to harmonic ground motion before expanding to numerical solutions for realistic ground motion. The first section is focused on covering a number of core topics and plugging some gaps in our understanding of SDoF dynamics before moving on to multi-degree of freedom (MDoF) systems in the next section.

Section 3 - Modelling Multi-DoF Systems

In section 3 we introduce the multi-degree of freedom system and the shear building dynamic model. We discuss the coupled nature of MDoF systems that makes them a challenge to model. We’ll explore numerical solution strategies by building our own DIY central difference algorithm and then implementing some off-the-shelf solution toolboxes.

Section 4 - Modal Analysis and Decoupling the Equations of Motion

In section 4 we cover the most important topic in the course - modal analysis. We’ll spend plenty of time here making sure you understand concepts like mode shapes, orthogonality and what it means to uncouple the equations of motion. You’ll see that modal superposition as a solution strategy offers us major advantages over the direct integration we discussed in the previous section. By the end of this section, you’ll have a deep understanding of modal analysis and be comfortable implementing it.

Section 5 - Damping Orthogonality

In section 5 we deal with damping. We’ll see that the same uncoupling of the equations of motion we discussed in the previous section cannot be directly applied to the damping matrix. In this section, we’ll explore how to derive a damping matrix that provides predictable levels of damping in each vibration mode. Although quite a short section, this one is important in equipping you with two complete and equivalent solution strategies; direct integration and modal superposition. We’ll finish out this section by demonstrating the equivalence of both.

Section 6 - Bringin it all together: N-storey response to earthquake ground motion

In the final section, we’ll take everything you’ve learned up to this point and build out the final capstone analysis code. At this point you’ll understand the theory and how it can be mapped into code - now we can emphasise coding efficiency and build a solution script that easily scales to larger numbers of degrees of freedom with no extra effort on our part.

By the time you complete this course, you’ll have a toolbox full of dynamic analysis tools and the knowledge and confidence to apply them to your own projects.

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2. Course prerequisites and do I need to know Python?