User`s guide

117
3. PROCEDURES
In order to determine the dynamic characteristics and elastic modulus of a vibrating
cantilever beam, the procedures of this experiment include research relevant data, initial
measurement of the beam, analytical estimations, hardware set-up, signal conditioning, testing
with LabVIEW program, taking measurements, and data analysis.
The information acquired from research and part of the measurement process should also
be used to produce uncertainty analysis and the contribution of each parameter to total
uncertainty.
3.1 Preparations
3.1.1 Research of Relevant Data and Initial Measurements
In order to estimate the natural frequencies of the cantilever beam, the material’s elastic
modulus and the density need to be found from professional sources. Research online, or use a
table in a textbook.
Measure the beam’s length and thickness. With a pencil, mark the location to install the
strain gauge on the beam at approximately 1 inch from the clamped end.
3.1.2 Undamped Natural Frequency
With the equations provided in Section 2, calculate theoretical undamped natural
frequency of the beam. Make sure to use the actual effective length of the beam for calculation.
The effective part of the beam is the “free vibrating” part between table and the free end.
3.1.3 Understand the Effect of Gain in the Signal Conditioner
Calculate the amplifier gain required to amplify the output of the Wheatstone bridge so that you
get 1 mV/micro-strain.
Recall Gage factor,
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Measured strain can be expressed as
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Recall the expression of change in bridge output voltage caused by a small change in resistance ,
Eq.73