Earthquakes and Multi-story Buildings – Understanding Modes and Natural Frequencies
0Day 3 | 1:30 PM–2:00 PM
"Earthquakes and Multi-story Buildings – Understanding Modes and Natural Frequencies"
Presented by:
Lynn Schreyer, Washington State University, Pullman WA USA
https://qubeshub.org/community/groups/simiode/expo/2025
Abstract: This is an experiential report on an end-of-semester project developed for a one-semester introductory course on Ordinary Differential Equations with a goal of understanding natural frequencies and modes of vibrations. We expand upon the earthquake problem (Earthquake Modeling Section of Kurt Bryan’s Differential Equations, A Toolbox for Modeling the World, textbook) to incorporate multi-story buildings and using experiments available on online Youtube videos. We begin by modeling the displacement of a series of 3 masses, connected using 4 springs; and calculating the natural frequencies and corresponding modes of vibration (eigenvalues and eigenvectors of the matrix of the resulting linear system). Next the results are compared with an experiment available online – the modes of vibration are consistent! We then move to modeling a 3-story building, as presented in a youtube video and compare the analytical results with those from the experiments. Even by assuming no damping, the results are remarkably similar, especially for the modes of vibration. The students are then asked to try changing the springs/mass values to increase the lowest natural frequency (avoiding typical earthquake frequencies).