next up previous
Next: Single Story Vibrations Up: m1index Previous: m1index

Introduction to Building Vibrations

image from Federal Emergency Management Agency

According to the US Geological Survey, the Earth sustains around 500,000 earthquakes a year, with 100 causing significant damage. This WEAVE module engages with the physics necessary to understand what happens to a building when an earthquake hits. You will learn about structural dynamics and the vibrations of buildings in order to mathematically describe the behavior of a three-story building in terms of its oscillatory response to earthquakes. This module uses imaginary and complex numbers, some linear algebra, and ordinary differential equations.

Module Objectives:

You will find that for a three-story building, one can describe building vibrations using a set of three second-order differential equations, similar to the spring-mass-damper equation that you studied in your first-year physics course. (The external link to that applet is here .) The key difference between the single-mass system you studied in physics, and the three-mass system here, is that the three equations used in the three-mass system are inter-related, or coupled. Physically, this means that the response and oscillations of one floor depends on the oscillations of all the other floors. In coupled systems, it is often convenient to write differential equations in terms of matrices. Matrix notation simplifies and unifies the mathematical description of dynamic systems like this three-story building. (If you need to review matrices, a recommended external site is http://www.morello.co.uk/matrixalgebra.htm.)

To get a general idea of what building vibrations are about, please view the videos of our small-scale building model oscillating at various frequencies. Right now this unfortunately requires Internet Explorer and Windows Media Player. Browser-independent versions of the video will be up soon.

The following videos for select sine wave frequencies are available.

Frequency Sine Wave Displacement Excitation

Size

File

2.35 Hz (75 kbps) 181 kB view (wmv)
3.2 Hz (75 kbps) 149 kB view (wmv)
6.2 Hz (75 kbps) 183 kB view (wmv)
6.9 Hz (75 kbps) 179 kB view (wmv)

All files compressed using Microsoft Windows Media Encoder using Microsoft MPEG-4 V3 codec.
Viewable using Windows Media Player 6.4+.

Studying the following sections will give you a deeper understanding of structural dynamics in terms of:



Subsections
next up previous
Next: Single Story Vibrations Up: m1index Previous: m1index