Lab: Measuring Beam Natural Frequencies

Lab #6

Lab #6 Measuring Beam Natural Frequencies

I. Summary

The purpose of this lab is to measure the natural frequency of a beam using a strain gage and an accelerometer. Using this set up, the free response time series data will be measured and will help aid in determining the natural frequencies of the beam. The first method involves determining the first natural frequency (ω1) of the beam by peak counting in the time domain. This will give a very rough estimate of ω1. The next method involves determining the first 3 natural frequencies (ω1, ω2, ω3) of the beam by a formal frequency domain analysis (fast Fourier transform). These experimental values of the natural frequencies of the beam will be compared to the calculated theoretical values of the natural frequencies of the beam that will be found using the equations shown in the next section. The calculated theoretical natural frequencies were 16.62, 103.75, and 290.50 Hz for ω1, ω2, and ω3, respectively. The ω1 found by peak counting in the time domain was 15.38 Hz. Finally, the FFT estimated natural frequencies were 14, 96, and 272 Hz for ω1, ω2, and ω3, respectively.

II. Data and Results

Table of Dimensions and Material Properties – Stainless Steel Beam

Density (kg/m^3) | Young’s Modulus (GPa) | Height off Table (m) | Length from Clamp (m) | Width (m) | Thickness (m) | I (m^4) | m (kg/m) |

7740 | 196.5 | .2429 | .39291 | .0127 | .00314 | 3.277E-11 | .3087 |

Theoretical Calculations

The first objective of this lab was to calculate the theoretical values for the first 3 natural frequencies of the stainless steel beam. These were found by using the following equation:

Where β1, β2, β3 = 1.875104, 4.694091, and 7.854757 respectively, E = Young’s Modulus of stainless steel, I = moment of inertial of the beam, L = length from clamp, and m = mass per unit length. In the table above, I and m were calculated so that each parameter could be inserted into the equation conveniently. The calculated...