In this short introduction section, I’ll set out a roadmap for the course and give you a sense of what to expect. This will give you a good idea of what we’re going to cover during this course. I’ll also briefly comment on assumed prerequisite knowledge - in other words, what you should have covered before taking this course, and also what you don’t necessarily need to know.

This 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 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 systems in the next section.

In section 3 we introduce the multi-degree of freedom (MDoF) 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 solutions strategies by building our own DIY central difference algorithm and then implementing some off-the-shelf solution toolboxes.

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.

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. This section is important as it equips 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. 

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.