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## Characterization of Cantilever Beam with Accelerometer

I. OBJECTIVES
In this lab you will:
1. Simplify a real system as an equivalent, single-degree-of-freedom system
2. Determine the natural frequency of a cantilever beam
3. Determine the influences of beam length and beam mass on the natural frequency of a cantilever beam
4. Compare your measured results to predictions of a mathematical model
Part 1: Characterize the cantilever beam system
2. Measure and record the width, thickness, length, and mass of the long and short cantilever beam assemblies using the calipers and scale. We will assume that the L-bracket bolted to the end of the beams are part of the beam since the mass of the beam is much greater than the mass of bracket.
Measure the mass of the accelerometer (excluding the cable) using the scale. Measure the mass of ten washer weights and the washer weight bolt and wing nut. Divide the mass of the ten washer
weights by ten to get an average mass for one washer. Assume each individual washer has a mass equal to the average.
Part 2: Build the experimental setup
1. Using the C-clamp, the adapter beam assembly (short piece of aluminum with a screw hole at one end), the long cantilever arm assembly, the accelerometer, and the bolt and ten washer weights, assemble the system shown in the pictures in Figure 4. We will ultimately deflect the beam in the direction parallel to the orientation of the washer bolt, so we want the screw in the adapter beam assembly to be tight (i.e., the beam is not to rotate about the screw like a pendulum). The accelerometer should be snug against the L-bracket, overtightening could break the accelerometer housing.
Figure 4. Pictures of the experimental setup.
2. Use the masking tape to run the wire from the accelerometer up the beam and onto the table as shown in Figure 4.
3. Wire the accelerometer to the 5 V supply and AI0 pinouts of the USB-6008 (see Background section for wiring information) using the DAQ jumper wires, alligator clips, and patch cables. We
MCEN 3047, Lab 4: Characterization of Cantilever Beam with Accelerometer
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will only use the Y axis output for this lab. Use a jumper wire to connect AI0- to the GND pinout to complete the circuit. Be sure the EXC+ and EXC- wires do not touch during the experiment or it will destroy the accelerometer. After wiring, connect the DAQ to the computer with the USB
cable.
Part 3: Setup MatLab to acquire data and perform experiments
1. In this lab, we’ll use the Data Acquisition toolbox in MatLab to capture and store the data. An excellent user interface for the toolbox has been created and posted to the File Exchange on the
2. Open MatLab. Under the Apps tab, select Data Acquisition Tool. We want to measure a voltage
from channel 0 of the analog input of the NI USB-6008 DAQ. After selecting the device, click Create Session.
3. Under the Session Properties tab, change the sample rate (Rate) to 10,000 Hz and the capture length (DurationInSeconds) to 10 seconds. These settings will instruct the DAQ to record data at a rate of 10,000 samples per second for 10 seconds.
4. Determine an appropriate distance to deflect your beam setup so as to not plastically deform the beam.
5. Release the beam and click Run Session. The experiment will record the data. When finished it will display the voltage vs. time signal on the plot under the View Data tab. Post-processing this
signal with a Fourier transform will yield the natural frequency of the beam.
6. After the plot appears and you are satisfied with the quality of the signal, select the Session Data tab. Click the Save Session Data button and save the matrix as long_10washers.mat.
7. Repeat the experiment for 8, 6, 4, 2, and 0 washers.
8. Repeat the above procedure using the short cantilever beam assembly.
9. Disconnect the USB cable from the computer before disconnecting the accelerometer.
Part 4: Tidy up
1. Disconnect all cables.
2. Close MatLab and power off all equipment.
3. Return your equipment to the storage rack.
V. DELIVERABLES
1. One lab report per group that provides background, summarizes the procedures, and presents and discusses the results of the experiment. Specifically:
a. Describe and develop a physical model to calculate the natural frequency of a cantilever beam as a function of meff and L. Discuss any intermediate calculations (I, meff, etc.). Compare
your calculations to experimental values (plot measurements and calculations of ωn vs. meff for short and long cantilever beams on the same plot). Perform a Fourier transform of your experimental time domain signal to determine the experimental values of ωn. Comment on variables you think introduce the largest amount of uncertainty.
b. How would you improve this experiment in the future?
c. Perform all analysis and figure generation in MatLab.
d. Refer to the documents posted to Canvas for formatting guidelines.