In this section, we’ll bring together what we’ve learned up to this point. So far we’ve written our code in a way that emphasises clarity at the expense of efficiency or scalability. But in this section, we’ll develop a dynamic analysis code that allows us to model the dynamic behaviour of a 30-storey building just as easily as a 3-storey building.

We’ll start by implementing the modal analysis techniques already discussed to identify and visualise all $N$ modes of vibration for a multi-storey structure. Then we’ll implement modal superposition to combine the modal responses into the final structural response.

Our code will utilise a piecewise exact numerical solution to identify the modal responses. This will allow us to simulate the response to an empirical ground motion. We’ll simulate the response of our system to the El Centro ground motion - but you can import and apply any ground acceleration record you want to apply to your structure.

After determining the structural response we’ll use simple equilibrium equations to determine the foundation shear force, overturning moment and foundation axial forces, all as a function of time. Although these are all very simple calculations they’ll allow us to quickly assess the overturning stability of our structure in addition to its dynamic response.

Finally, we’ll put our new animation skills to good use and build out an animation of the dynamic response of our structure. After this, you’ll be able to easily expand this to build out a visualisation and animation of any quantity you like.