Figure 1

Figure 1

Hello. Yes, this is Wayne Tustin. Sometimes I’m called “Mr. Random Vibration”. Other times I’m called “Mr. Multi-Axis Vibration Testing”. Those are two points I emphasize in my short courses, such as next week in Michigan for the SAE and a week later in Florida. Also via CD-ROM, with lessons coming to me via e-mail. We thank Bruel & Kjaer for this Web time and the Chicago Chapter of the Institute of Environmental Sciences and Technology (IEST) for arranging these presentations and for inviting me. Our subject today is “What is RESONANCE all about?”


Figure 2

Figure 2

Why discuss resonance? Because unless resonance is involved, vibration never causes any damage. Also, many people define the study of vibration as the study of resonances. Let’s get started.


Figure 3

Figure 3

This is a mass. It’s an unusual mass in that (theoretically) it has no springiness, while …


Figure 4

Figure 4

… This is a spring. It’s an unusual spring in that (theoretically) it has no mass.


Figure 5

Figure 5

Put them together, along with some friction or damping, and we have a single-degree-
of-freedom, SDoF, system. Note the guides that restrict the mass, when you excite the system, to vertical motion only.

Another simple system, not shown, is the pendulum. Visualize yourself pushing a child in a swing. You experimentally discover that if you adjust your forcing frequency Ff to match the swing’s natural frequency Fn , little force is required to develop large oscillatory displacements. Has everyone had that experience?


Figure 6

Figure 6

Let’s invert SDoF system and attach it to a shaker. We’re going to measure both the response acceleration on the sprung mass and the input acceleration on the shaker table. We’ll divide the former by the latter as we vary the forcing frequency Ff . The ratio between response and input is called “transmissibility” or “magnification”, which we will plot in slide 9.


Figure 7

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Figure 7

Here in this video clip, we’ve pre-adjusted the shaker’s forcing frequency Ff to match the SDoF system’s natural frequency Fn , so that little force is required to develop large oscillatory displacements.

Click on the image to see this video clip.


Figure 8

Figure 8


Figure 9

Figure 9

Here we have a family of transmissibility graphs. The shaker of Slide 7 was adjusted to make Ff = Fn, so that “transmissibility” or “magnification” was maximized. There are several graphs plotted here. The amount of friction or damping differs between graphs. If there were no damping, the graph would go off the page (infinite transmissibility). In slide 7, the shaker excitation was sinusoidal, single-frequency.


Figure 10

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Figure 10

But the excitation here in this video clip, during liftoff of a rocket, is strongly random. We first became aware of random vibration when we tried to launch early rockets. Failures led to today’s random vibration testing and to today’s almost routine successful launches.

Think back, please, to the single-frequency-
at-a-time sinusoidal shaker vibration of slide 7. You know what a sine wave looks like, in the time domain, on your oscilloscope. Here in slide 10, however …

Click on the image to see this video clip.


Figure 11

Figure 11

… the excitation is seen, in the time domain, to be random, non-repetitive. As a result, in the frequency domain, slide 14, the vibration spectrum will be seen to be continuous, to contain all frequencies, simultaneously.


Figure 12

Figure 12

Contain all frequencies, simultaneously? That’s hard to believe, isn’t it? Let’s go back to your high school or physics class, where the teacher passed a beam of white light through a prism, creating a display of all colors, all wavelengths, all frequencies of visible light. Remember? Similarly, random vibration contains all frequencies, simultaneously. Let’s come back from space to…


Figure 13

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Figure 13

… this video clip, taken in Detroit, but I’ll bet you know some rough roads in your area. Visualize three accelerometers on one axle, recording fore-and-aft, left-and-right, and vertical vibration, as seen in…

Click on the image to see this video clip.


Figure 14

Figure 14

Here they are, fore-and-aft, left-and-right, and vertical vibration, all in the time domain, as on your oscilloscope. Down at the bottom, we see the three records in the frequency domain, on a spectrum analyzer, plotted as ASD or PSD vs. frequency. Note the broad spectrum, containing all frequencies 1-100 Hz, tapering off to perhaps 200 Hz. Vertical is most severe. What is the effect of such continuous spectrum vibration?


Figure 15

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Figure 15

Here in this video clip you see two reeds pointing at you. With single-frequency-at-a-time sinusoidal shaker forcing at 22 Hz, we see the red reed responding strongly. Eventually this reed will break, right? Fatigue failures are not our goal here.

Click on the image to see this video clip.


Figure 16

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Figure 16

Here in this video clip you see the effect of single-frequency-
at-a-time sinusoidal shaker forcing at 34 Hz. Note that the white reed responds strongly. Eventually this reed will break, right? Again, fatigue failures are not our goal here. Please note that, because of the geometry, one reed or the other reed or neither reed, will respond. The reeds cannot collide, right? But visualize what will happen if the shaker vibrates simultaneously at all frequencies.

Click on the image to see this video clip.


Figure 17

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Figure 17

Here in this video clip the shaker excites the reeds at all frequencies 1-100 Hz, simultaneously. Both reeds respond. If we had sound, you could hear them collide. What kind of physical unit might these reeds represent?

Click on the image to see this video clip.


Figure 18

(Illustration – courtesy C. Felkins)

Figure 18

Visualize this card cage being sinusoidally excited left-and-
right. At ff1, one of the printed wiring cards responds, left-
and-right. At ff2, another of the printed wiring cards responds, left-and-right. At ff3, another of the printed wiring cards responds, left-and-right. None moves far enough to strike its neighbors. The unit passes a sine vibration test. But the unit is known to fail in flight. So, in our lab, let’s excite it with random vibration. Now the cards collide, much as they do in flight. The unit fails a random vibration test.


Figure 19

Figure 19

Look at these three time histories. They were recorded simultaneously in a building’s basement, on an upper floor and inside an equipment on that floor. The mixture of earthquake frequencies at ground level, reaches 0.23g peak. One frequency in particular excites floor resonance, exciting a peak response of 0.63g. Someone made an error and mounted, on that floor, an equipment having the same natural frequency as the floor. Note that inside the equipment, response reaches 4.22g. Someone has violated Rule #1 of dynamic design: THOU SHALT NOT STACK THY RESONANCES!! Please write down that rule!!

The automotive folks I teach next week place their instrument cluster natural frequencies where there is little instrument panel resonance. They place their instrument panel natural frequencies where there is little body bending and twisting. They place their body natural frequencies where there is little suspension resonance. They all avoid stacking resonances. You should do the same.


Figure 20

Figure 20

Here are some upcoming “open” courses which you might attend. Santa Barbara in February is not considered to be punishment! I’m lucky to live there. While you are at this website, please see the details of these courses by clicking here. Or consider having us “tailor” training to meet your needs, for presentation at your site, as last month at Redstone Arsenal and at Daimler-Chrysler. Details about CD-ROM training are also shown.


Figure 21

Figure 21

Thanks again to B&K and to IEST!

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