Sample Lab Report
The following is a sample lab report for a modified version of Experiment V1. Please read it over
to understand what is expected of you for each of the lab reports. As discussed in the syllabus,
the labs will be graded on neatness and grammar in addition to the accuracy and presentation of
your results.
Aspects to note:

Do not use first person (I, we, etc.) in your lab report.

Text accompanies all of your results, even sections that are primarily figures and tables.

The Executive Summary describes the complete experiment in one concise paragraph.
Results and a brief (typically only one sentence) conclusion are also stated.

The figures are properly titled, labeled and are placed in the document so that the reader
can easily understand them.

Figures, Tables, and References are cited in the body of the text (but not in the executive
summary).

Be conscious of your significant digits. Results do not have to be stated to 9 or 10 decimal
place accuracy.

The lab report does not have to be long, but it does have to be complete.
Stiffness Measurements for a Cantilever Beam
Your name
Lab Section:
Group A, 10:00am
Group Members:
Date of Experiment
Executive Summary
The objective of this experiment was to determine the stiffness of a cantilever beam from the
measured natural frequency. The test specimen was a 19.29 inch cantilever aluminum beam with
a 0.253 inch by 1.02 inch rectangular cross section. A 0.483 lb weight was placed on the free end
of the beam and the frequency response function was measured using a real-time spectral
analyzer. The natural frequency of 8.63 Hz was measured from the maximum amplitude of the
frequency response function. A beam stiffness of 3.698 lb/in was computed using the measured
natural frequency and the measured tip mass, while a stiffness of 5.752 lb/in was computed using
the measured dimensions of the cantilever beam. This 35% difference between the measured and
predicted values of stiffness was attributed to two primary sources of error: measurement error in
the beam dimensions and an invalid assumption in the expression for the predicted value of the
stiffness.
Objective
The objective of this experiment was to determine the stiffness of a cantilever aluminum beam
from the measured value of its natural frequency.
Procedure
The test specimen was an 1.020 x 0.253 x 19.291 inch aluminum beam clamped at one end. A tip
mass and accelerometer were attached to the free end of the beam, and an impact hammer was
used to excite the structure for real-time spectral analysis. The procedure for the experiment was
as follows:
1.
The distance L between the fixed end and the tip mass was measured with a steel ruler.
2.
The tip mass was removed and weighed using a beam balance. The tip mass was then
reattached to the free end of the beam. The accelerometer was also attached to the tip
mass with a small amount of wax.
3.
The width and thickness of the beam was measured with a set of calipers.
4.
An impact hammer test was then performed using the real-time spectral analyzer. The
beam was struck softly with the impact hammer at approximately ½ of its length.
5.
The frequency response function was obtained by taking five averages and exporting the
result to a text file.
6.
The text file was then transferred into Excel format and saved to the hard disk under the
name dleo.xls.
Results and Analysis
Table 1 lists the measured beam dimensions and the measured mass of the weight attached to the
tip.
Table 1 - Measured Beam Properties
Thickness
0.253
in
Width
1.020
in
Length
19.291
in
Tip Mass
1.25E-03 lb-sec^2/in
The measured frequency response between the acceleration of the tip mass and the location of the
input excitation is shown in Figure 1.
magnitude (in/sec^2/lb)
10000
1000
100
10
0
10
20
30
40
50
frequency (Hz)
Figure 1: Measured frequency response function. Peak value is denoted by a black circle.
The natural frequency corresponds to the peak value of the frequency response function. This
value was determined to be 8.63 Hz for the measured frequency response shown in Figure 1. A
black circle in the figure denotes the peak value of the frequency response function.
The stiffness of the vibrating beam was estimated from the measured natural frequency and the
given tip mass. Using the stated value for the tip mass, 219.8 g or 1.25x10-3 lb-sec2/in, the beam
stiffness was estimated from the equation


k  M n2  1.25 x10 -3 (( 2 )8.63) 2  3.698 lb/in .
The stiffness of the beam was also estimated using the equation
k  3EI
L3
where E is the Young’s Modulus of aluminum, I is the moment of inertia of the cross section, and
L is the length of the beam. Substituting 10x106 lb/in2 for Young’s Modulus (see Reference 1),
and I = 1.38x10-3 in4 for the moment of inertia, and L = 19.29 in for the beam length, yields k =
5.752 lb/in.
Discussion and Conclusions
1. Using L = 19.291 in, t = .253 in, and b = 1.020 in for the length, thickness, and width of the
beam (see Table 1), respectively, and using 0.098 lb/in3 as the weight density [1], the mass of
the beam was estimated to be
mb  19 .291 0.253 1.020 (0.098 ) / 386 .4  1.26 x10 -3 lb  sec2 /in.
The estimated value for the beam mass was on the same order as the tip mass (1.25x10-3 lbsec2/in), therefore the assumption that the beam mass is much greater than the tip mass is
invalid.
2. The beam stiffness computed from the measured natural frequency and the given mass is
approximately 35% lower than the stiffness value predicted from the equation stated in the
lab handout. Possible sources of error include incorrect measurement of the tip mass and
beam parameters. Error could also be present due to the fact that the tip mass was not
significantly greater than the mass of the beam, invalidating one of primary assumptions
regarding the equation for the beam frequency. A more accurate equation would be required
to determine the effects of beam mass on the estimate of the beam stiffness.
References
1. Ashby, M., Jones, R. H., Engineering Materials, Pergamon Press, Oxford, 1980.
Appendix
Note to Students:
This section would contain the original data sheet for the lab in addition to any calculations
specified by the lab handout. Calculations placed in the appendix can be handwritten in
pen.