In this section, we start our study of multi-degree of freedom systems. We kick things off by recognising that all structures are in fact continuous systems and that considering them as a collection of lumped masses is an approximation of this reality. Then we consider the advantages of a MDoF model over a SDoF model and what the extra complexity gives us.

After establishing why we might opt for a MDoF model, in the next lecture we set about deriving the equations of motion for a multi-storey structure modelled as a MDoF shear building.

Once we have a system of coupled differential equations that describe the motion of our shear building - we need to solve them. This presents us with a challenge since our equations are coupled and the motion of any one mass is influenced by its neighbours. This leads us to numerical integration. After reviewing the underlying theory, we’ll implement our own DIY central difference algorithm.

Once we’ve implemented our own central difference algorithm, we solve the equations in the next lecture and visualise the vibration behaviour of our multi-storey structure subject to harmonic excitation.

In the final lecture in this section, we introduce some off-the-shelf tools for solving differential equations and apply them to our structure. We took the time to understand, from the ground up, how to implement a numerical solution in the previous lecture - with this under our belt, this lecture is about showing you how you can make use of well-established tools for better efficiency.