SETUP I: CORD. Continuous Systems

Transcription

1 Lab #8 Continuous Systems Name: Date: Section / Group: SETUP I: CORD This part of the laboratory is mainly exploratory in nature. By using your hand to force the cord close to one of its ends, you should attempt to excite it at its first, second, third, etc., natural frequencies. You should be able to feel that it takes very little effort (force) to keep the system moving at a resonance. This is a consequence of the inertial forces balancing the stiffness forces, so it feels as if little or no force is required to cause a deflection. 1. (10%) Why is some force required to keep the cord oscillating at a resonance? 2. (10%) Sketch the first three mode shapes. Lab #8 Continuous Systems page 1 of 6

2 3. (10%) You should also experiment with an impulse applied to one end of the string and view the resulting travelling wave motion. Try plucking the cord or applying a series of periodic impulses. If properly excited different mode shapes will appear. Try different tensions. Comment on how you think a wave, or series of waves, is related to a mode shape. How does this relate to, say, plucking a guitar string? SET UP II: BEAM Switch on the shaker power supply and refer to the Frequency Sweep Instructions provided at the experimental set-up. If at any time you start to hear a knocking sound, hit the ABORT button immediately. The objective here is to determine the natural frequencies and associated mode shapes of the beam via a frequency sweep. The frequency sweep will start at 2.0Hz, step incrementally at a rate of 1.0 Octaves/Minute (i.e., a logarithmic sweep rate that takes one minute for 1Hz to 10Hz, 10Hz to 100Hz, 100Hz to 1000Hz...), stop at 200Hz, and then reverse the sweep direction. 4. (10%) Find the values of the natural frequencies that lie between 2Hz and 200Hz and sketch the associated mode shapes, pointing out the nodes and the location of the applied force. Lab #8 Continuous Systems page 2 of 6

3 SETUP III: CABINET Though there are specific procedures to complete in this part of the laboratory, you should use the equipment supplied to further explore the behavior of the system. Attach the accelerometer to any part of the structure and feed its signal through the scope and into a VI to take its FFT. Set the sampling rate of the VI to 1000Hz. 5. (10%) Hit the structure with your knuckle and obtain the FFT of the response. Make a hard copy of the FFT and then repeat the procedure. Comment on the differences and similarities of the two FFTs you obtained and explain the reasons for the similarities/differences. The various peaks evident in the FFT of the accelerometer s signal represent resonant responses to the impact you gave the system. Ask your consultant to discuss the form of the impact you used and to present other methods that are used to impart energy into systems under test. 6. (5%) List any five of the natural frequencies of the system. Lab #8 Continuous Systems page 3 of 6

4 7. (5%) If the accelerometer were moved to another location, how would the FFT of its signal differ from that obtained in question (6)? Under what condition might we fail to detect a natural frequency of the system (HINT, think of mode shapes)? The cabinet that we are studying has a shaker attached inside it. Using the signal generator provided, drive the shaker with a sinusoidal signal and check the natural frequencies listed in question (7) do in fact correspond to resonances. You should be able to clearly hear when a resonance is excited, but also view the accelerometer signal on the scope to check that a large amplitude has been obtained. 8. (10%) Is the shaker guaranteed to excite all the resonances? Explain. 9. (5%) How does stiffening the structure with your hand change a natural frequency. Lab #8 Continuous Systems page 4 of 6

5 Force Force 10. (5%) Change the sampling rate for the FFT to 2000 Hz. Describe how this affects the analysis. 11. (5%) Sketch what you think the approximate time histories of an impact with a soft and a hard hammer would be (try this experimentally). Discuss what the differences Soft Hammer Hard Hammer Time Time would be in the responses of a system hit by each of these two types of hammers. Lab #8 Continuous Systems page 5 of 6

6 12. Discuss with the consultant how a modal analysis test would be completed in practice and the concept of normalizing the response by the applied force. 13. (10%) Describe some applications of the vibration of continuous systems related to everyday objects that you have experience of. Lab #8 Continuous Systems page 6 of 6