LAB #8: Vibration of Beams Equipment: Remember to record serial numbers of the equipment you use! Dell Optiplex computer with National Instruments Pentium PC with NI PCI-MIO-16E-4 data-acquisition board NI BNC 2120 Accessory Box VirtualBench Instrument Library version 2.6 Impulse-Force Hammer (PCB 086C03) Red Vinyl Tip, White Nylon Tip, and Blue Vinyl Cover Piezoelectric Accelerometer (PCB 302A) Four-channel Amplifier/Signal Conditioner Unit (PCB 482A16) Objectives: • To introduce you to the use of frequency response functions for determining the natural frequencies and mode shapes of a vibrating structure. 1. Natural Frequencies and Mode Shapes of a Cantilever Beam In this part of the laboratory exercise you will obtain three frequency response functions (FRFs), which constitute part of the data that would be taken in a modal test. These frequency response functions can be used to determine approximate values of the lowest two natural frequencies of the cantilever beam with tip mass (the accelerometer). The accelerometer will be mounted near the tip of the beam on the underside of the beam. The impulse hammer will be used to tap the beam at three locations -- location A (2 in. from the tip of the beam), location B (5 in. from the tip of the beam), and location C (8 in. from the tip of the beam). Impulses at these locations will excite different modes or combination of modes in the beam. 2. Beam, Accelerometer, and Impulse Hammer Set-Up Set up the beam, accelerometer, and impulse hammer for the beam acceleration FRF tests. 2.1. Make sure that the aluminum beam is securely clamped in the bracket that is bolted to the steel loading frame. The edge of the clamp should be at right angles to the axis of the beam. Assume that the modulus of elasticity for the aluminum beam is E = 10 ×106 psi and that the weight density is ρ = 0.10 lb/in3. Note down other quantities that you might need to analyze your experimental data. 2.2. Attach the PCB accelerometer to the bottom side of the beam. Carefully connect the accelerometer to the PCB amplifier/signal conditioner. Set the amplifier gain of this accelerometer channel to ka = 10. Connect the amplifier output to the A/D converter. 2.3. Install a white-nylon/blue-vinyl tip on the impulse hammer force cell, and connect the hammer to the PCB amplifier/signal conditioner. Set the amplifier gain of this force channel to kf = 10. Connect the amplifier output to the A/D converter. Have the TA check your set-up of the beam, accelerometer, and hammer.3. Spectrum Analyzer Set-Up Use the Virtual Bench Digital Signal Analysis program to capture and analyze the data from this experiment. Do you remember how to set the acquisition parameters? Review the instructions from Lab 6. In particular, pay attention to the sampling rate and the block size; you can estimate the required sampling rate by determining the expected maximum signal frequency. 4. Time Histories of Impulse Force and Acceleration Acquire the time history of the impulse force and the time history of the acceleration of the tip of the beam as you strike (tap) the cantilever beam at three different locations. 4.1. Tap the center of the top surface of the beam 8 in. from the tip of the beam (location C), using the same “good technique” you developed in Lab #7. If you don't get a “trigger,” call on the TA to help you. There should be a single impulse peak for the time history of the force signal, and the time history of the acceleration should appear to be the superposition of a high-frequency sinusoidal signal and a low-frequency sinusoidal signal. When you think you have acceptable time histories of acceleration and force, show your graphs to the TA before continuing. Save your data to disk. 4.2 Repeat with two additional taps, one at the center of the top surface of the beam 5 in. from the tip of the beam (location B), and the other at 2 in. from the tip of the beam (location A). When you think you have acceptable time histories of acceleration and force, save the data to disk. 4.3 Experiment with different sampling rates to see the effect on the acquired signal. 5. Impulse-Force Spectrum and Acceleration FRFs Acquire the amplitude spectrum of the signal from the hammer and frequency response of the accelerometer signal. In order to accomplish this, you must set the DSA appropriately. Then excite different modes in the cantilever beam by tapping at the same locations as in Section 4. Note that, since you are not asked to do a ratio calibration of the hammer/accelerometer pair, the units for these FRFs will be VoltsVolts. Remember to save the spectra of the hammer and the accelerometer signals for each tapping location. The spectra will reveal features of the beam response that you can interpret. 6. Play You might want to consider impacting at locations other than those suggested above. You sould see some high frequency signals of rather large amplitude. Try to figure out where these come from. The TA will give you some clues.Homework Exercises: (To be turned in to the TA in two weeks.) 1. Make hard-copy plots of the graphs that you saved during this lab exercise. 2. Calculate the first three natural frequencies (in Hz) of a bare cantilever beam having the dimensions of the beam used in this exercise. 3. Make a table that lists the first three natural frequencies of the bare beam, as calculated in the previous step, the natural frequency(ies) from the FRF obtained by tapping the beam at point “A,” the natural frequency(ies) from the FRF obtained by tapping the beam at point “B,” and the natural frequency(ies) from the FRF obtained by tapping the beam at point “C." 4. Discuss quantitatively the loading effects produced by the mass of the accelerometer attached to the beam. 5. Using rough sketches of the first and second natural modes of the beam, discuss the significance of the relative amplitudes of the various peaks that appear in the three FRFs. 6. What was the source of the high frequency
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