Class: BE310
Group: T1
Members: Kinnari Chandriani, Michael Jue, Vikram Krishnan, Naila
Machado
Date: May 2002
Abstract:
The purpose of this experiment was to confirm the relationship between
the fundamental mode frequency of a vibrating bar, and the actual mass
attached to its end, in a horizontal cantilever beam set up.
At the zero mass added state, the measured values of the “c” coefficient
factor of the mbar term for bars 1, 2, and 3, were 0.335 + 0.032 (95 %),
0.298 + 0.037 (95 %) and 0.413 + 0.139 (95 %) respectively. These
all overlapped one another within 95%, but were all slightly, and significantly,
higher than the predicted value of 0.25. Still, this proved that,
within 95%, there was a single “c” value which was reasonably close to
0.25, confirming a beam theory type relationship at the zero mass state.
It was not possible to add a mass to the bar which was overwhelmingly
higher than the mass of the bar itself, so a relationship could not be
confirmed at this state, though it was suspected that it would follow a
spring theory relationship.
The “c” values were used to construct theoretical plots using
a formula which combined the mass of the bar and the mass added.
T-tests proved that these plots matched the experimental plots of fundamental
mode vs. 1/sqrt(massbar + c*massadded). This confirmed the combined
formula for a cantilever beam with a mass added of: