Effects of Stiffness and Density on a Material's Natural Frequency

Overview

Objectives/Goals My objective was to find whether stiffness, density, or both, affected a material's natural frequency. Methods/Materials First, I gathered five springs of different stiffness' and eleven different weights. By hanging weights on the end of spring, I determined the natural frequency. I did this by pulling the weights down and releasing them, measuring the spring's vertical motion in cycles per second. I then graphed my test results, finding a mathematical relationship between stiffness to frequency and mass to frequency. Results From the graphs of my test data and the equation of each trendline, I made an equation using both stiffness and mass to determine a material's natural frequency. I made this equation so that I would be able to find the natural frequency of any object using it. My equation was Frequency = 0.346 (stiffness^ 0.4072/ mass^ 0.486) Conclusions/Discussion I looked up the real frequency equation in a math book and found that: Frequency = ½'pi' or 0.159 (stiffness^0.5/mass^0.5). I found that the equation I had derived was slightly off. Using my equation, I could find the natural frequency of any given structure, such as a fence, bar, or even building. The concentrated mass on the end of each spring represented, and served the same purpose as, the density of any given structure.

Awards (1)

• Category Award

Competition history

• CSEF 2003 Applied Mechanics/ Structures & Mechanisms/ Manufacturing · Entry J0230

Resources

• CSEF project summary ↗

Related projects

Closest projects by meaning, across every fair and year in the corpus.

Browse more like this

• All Engineering projects
• CSEF Engineering projects
• Every CSEF 2003 project