Fundamental Frequency of Beam
Logan R. Graves
Introduction
In this lab the fundamental frequency of a simple aluminum beam was measured. This was
done for two cases of support, the beam being simply supported and the beam as a
cantilever. An impulse hammer was used to provide input stimulation, and the behavior of
the beam was measured using an accelerometer attached to the beam
Beam Characteristics
Width
Thickness
Length
25.6 mm
7.14 mm
560 mm
Results
Simply supported
The results for the beam being in a simply supported position are shown below. The
accelerometer was placed in the middle of the beam for this test.
Table 1.1, Simply Supported Results
Item
Value
Units
Time @ peak 1
111.23
ms
Time @ peak 2
455.762
ms
Amplitude @ peak 1
6.057
g
Amplitude @ peak 2
2.862
g
344.532
ms
Delta t
# of periods between 1 and 2
44
Period of oscillations E/F
7.83
ms
Damped natural frequency
802
rad/s
Natural frequency
802
rad/s
94
g
Stiffness
60600
N/m
Damping
0.286
N/(m/s)
754
rad/s
Equivalent mass
Natural frequency estimation
Cantilever
The results for the beam being in a cantilever position with the accelerometer placed at the
end of the beam are shown below.
Item
Value
Units
Time @ peak 1
91.113
ms
Time @ peak 2
845.801
ms
Amplitude @ peak 1
1.268
g
Amplitude @ peak 2
1.176
g
754.688
ms
Delta t
# of periods between 1 and 2
11
Period of oscillations E/F
68.6
ms
Damped natural frequency
91.5
rad/s
Natural frequency
91.5
rad/s
Equivalent mass
113
g
Stiffness
947
N/m
0.016
N/(m/s)
123
rad/s
Damping
Natural frequency estimation
Conclusion
The stiffness of the beam when it is in a simply supported position is far larger than the
stiffness of the cantilever beam. This is expected. Further, fundamental frequency of the
cantilever is far smaller than that of the simply supported beam. Another interesting result
was that the Rayleigh method of estimation for the natural frequency was fairly close to the
actual value.