In this Python mini-project, you’ll learn about the Duhamel Integral and how it can be used to simulate the dynamic response of a single degree of freedom system. We’ll discuss how to solve the integral and then write some Python code to implement our solution for any arbitrary loading. In the second half of this project, we’re going to use our Duhamel Integral solver to build a crowd loading simulation. This will allow us to simulate the vibration response of a footbridge to pedestrian traffic.
By the end of this post you’ll understand when and why a dynamic analysis is performed instead of a (usually more straightforward) static analysis. Although we typically encounter static loading, dynamic loads occur with sufficient frequency that we need to understand how to assess their influence on a structure. Typical forms of dynamic loading can include loading due to earthquakes, wind, vehicle or pedestrian traffic or wave loading on coastal or offshore structures.