Distance Learning's Sample Lesson - page 6
Your listing of natural frequencies probably resembles Figure
10-5.
| Number of Nodes | Mode # | Hz |
| 0 | 1 | 7.5 |
| 1 | 2 | 84 |
| 2 | 3 | 268 |
| 3 | 4 | 557 |
| 4 | 5 | 940 |
Figure 10-5 Natural Frequencies of Cantilever Beam
I’d like to ask you a question:
How many natural frequencies does this beam have? I hope you answered "an infinite number".
That is correct. If we have the right source of vibration, and a technique for identifying the modes, we will find a large number of modes. Recognize, though, that the nodes and antinodes must get very close together.
In your laboratory work, you have perhaps noticed that moving an accelerometer a small distance can give vastly different results, especially at the higher test frequencies. You might move from a location close to one resonance’s node to a location close to its antinode and at the same time from a location close to another frequency’s antinode to a location close to its node.
Seeming Lack of Order
Were you earlier disturbed by the seeming lack of order in the series of natural frequencies you observed on the cantilever beam 7.4 Hz, 84 Hz, 268 Hz, 557 Hz, 940 Hz, etc.? Many people anticipate a 1:2:3:4:5.... harmonic relationship in that series. It never occurs, except in one very limited class of structures ...... cables under tension.
In the course we ask participants to visualize a cable under sufficient tension to make mode #1 occur at 256 Hz, mode #2 at 512 Hz, mode #3 at 768 Hz, mode #4 at 1024 Hz, etc. Exaggerated line drawings show how the cable flexes at each of these modes.
Then we ask: where would you find a cable having those natural frequencies?
Figure 10-6 Strings of a Grand Piano
Cables have their uses, but flat plates come closer to the hardware most of us work with. Do vibrating plates warp and bend? They sure do. Measuring those responses is one of the things we do with strain gages and accelerometers.
Figure 10-7 shows four of the many possible modes in which a flat slab (an optical table) responded to some input.
