# Simulation of a two storey structure under dynamic loads

## Summary

The activity is part of a first year course for Engineering Science students at the University of Toronto called ESC103F: Engineering Mathematics and Computation. In this computer lab activity, students use MATLAB to simulate and analyze the dynamic behaviour of a two storey structure under free vibration.

## Learning Goals

Students learn to numerically solve a system of differential equations describing the dynamic behaviour of a two storey structure.

Students learn to write a MATLAB program to numerically solve this system, to plot the time domain results, and to analyze the results in the frequency domain.

The higher order skills being developed are primarily related to the integration of subject matter across the curriculum.

## Context for Use

First year university level at a research intensive university. Class size ~300.

This is a two-hour computer lab activity.

Students are introduced to the basics of programming in MATLAB as part of this course and make use of these basic programming skills to write their own m-file to simulate this system.

This lab activity is designed to integrate ESC103F with two other courses the students are taking in the same semester: CIV102F: Structures and Materials - An Introduction to Engineering Design, and MAT194F: Calculus I.

The activity is situated towards the end of the ESC103F course once the students have learned some basic linear algebra as well as how to numerically solve initial value problems using the Euler method.

## Description and Teaching Materials

The handout that has been uploaded describes the lab activity in three parts.

The first part is what the students receive prior to the lab. A schematic representation of the two storey structure is given followed by a simplified "Lollipop" model of the structure on which the mathematical model is based. This part also contains a complete description of the lab activity.

The second part is a follow-up announcement I sent to the students after the lab showing my results in both the time domain and the frequency domain. This part also contains a link to a YouTube video showing a physical model of a three storey building being forced sinusoidally at its base.

The third part is a second follow-up announcement that goes into more depth on the analysis portion by linking the eigenvalues of the system's state matrix to the resonant frequencies observed in the simulation.
Using MATLAB to simulate and analyze the dynamic behaviour of a two storey structure under free vibration (Acrobat (PDF) 75kB Sep27 16)

## Assessment

No assessment is made based on this lab activity. A test is given towards the end of the course where students are asked to use MATLAB to simulate a dynamic system they have not seen before.