REALLY? ALL FREQUENCIES AT THE SAME TIME?

Some faithful readers of this column will recognize that much of this idea appeared in TEST Aug-Sept 2012 in slightly different form. Will you forgive me for using it again, very slightly modified? This avoids you having to look through your stack of carefully preserved back issues?

It’s 8am on the third Monday morning, here in the conference room of A-1 Environmental Testing Lab. Once again test engineer Joseph A. “Joe” Youngman, hero of this series, is ready to briefly address his coworkers, aiming to make random vibration testing less mysterious. Nearly every department of A-1 is represented.
“Good morning, fellow workers, to the third of our five sessions. Several hallway conversations this past two weeks have told me that one-test-frequency-at-a-time sine vibration testing is credible. But some of you have warned me that I’ll have trouble convincing you of today’s topic: that when we perform random vibration tests, that our shaker’s armature is vibrating at all frequencies simultaneously.” Nearly all his audiences’ heads are nodding.
“By 8:30, I hope that you’ll feel that all-frequencies-simultaneously-vibration is possible. Then I have two more Monday mornings to tell you about early random vibration tests and about how “Al” Jenkins currently performs our random vibration tests.”
Understanding spectrum
“Let’s start with this figure, taken from a customer’s test needs.”
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Joe gives his audience a few seconds to examine the figure, then continues, “This graph calls for random vibration having a spectrum of 10-2,000 Hz. Do you perhaps envision that our shaker’s sinusoidal vibration at 10 Hz is somehow mixed with some sinusoidal vibration at 11 Hz + some sinusoidal vibration at 12 Hz + some sinusoidal vibration at 13 Hz + some sinusoidal vibration at 14 Hz + some sinusoidal vibration at 15 Hz, etc. all the way out to sinusoidal vibration at 1,998 Hz + some sinusoidal vibration at 1,999 Hz + some sinusoidal vibration at 2,000 Hz?” Joe looks at the individual members of his audience. Nearly all nod their agreement.

“Well,” comments Joe, “that mental picture is not quite right. I can sympathize with you, because I once had that same erroneous mental picture.” Joe waits a few seconds.
“But it’s not quite right. I’ve got two PowerPoint slides to show you. They deal, not with mechanical vibration, but rather with optics.” Here Joe snaps on his video projector and Figure 20.8.1 appears on the conference room wall.

Continuous spectrum – a difficult concept
“The concept of a continuous spectrum, a spectrum with no ‘holes,’ of vibration occurring simultaneously at all frequencies, is somewhat difficult for newcomers to random vibration.

“Perhaps this will help. Recall in high school physics how your instructor beamed white light through a prism?” Joe waits while audience members think back to high school physics.

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Figure 20.8.1 Visible light spectrum

“And then did he or she point out that the light beam was bent in passing through the prism?” Again Joe waits while his audience members think back……….. some of them many years back.

“Do you remember the continuous spectrum of colors thrown onto the wall?” Joe asks.

“Oh, yes, I remember that,” agree several coworkers.

“You accepted the idea,” Joe continues, “that the white light contained all visible wavelengths, all visible frequencies.”

 

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Figure 20.8.2 Visible light spectrum

“I hope that today you can accept the idea that random vibration is somewhat similar.” A few audience members nod tentatively.

After 10 seconds silence, Joe continues, “You may be interested to learn that that Sir Isaac Newton (1642-1727) is credited with being the first to thus show that white light is composed of many colors – various wavelengths – various frequencies. He is also credited with coining the word “spectrum” for such a display.
But that’s not vibration.
Joe waits until one of his listeners objects, “But that’s not vibration.”
To which Joe agrees, and slowly proceeds. “You’re right. That’s white light, not mechanical vibration. But if you’ll accept the idea that white light contains light of many colors, many wavelengths, many frequencies, somehow mixed together, maybe (stretching out the word to ‘maaaybeee’) you can accept the idea that white random vibration, such as Figure 22.5.1 asks for, must contain vibrations having a range of frequencies.”
If not sine, what?
That listener questions Joe further. “Well, if the waveforms aren’t sinusoidal, what are they?”
To which Joe slowly answers, “I kind of hoped that we’d not get into this, because I’m not real sure how best to answer your question, but they’re kinda like the waveform appearing on an oscilloscope when someone coughs into an attached microphone—you know, like you see on some TV commercials advertising cough medicine. If such a fraction-of-a-second waveform were converted to an electrical signal and made continuous over time, then applied to a loudspeaker, you would hear a dull roar.” (Dennis Nelson analogy.) “You may have heard such a roar coming from one of A-1’s shakers during a random vibration test.”

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Figure 20.2.2 “Random” means unpredictable

After a few silent seconds, Joe proceeds. “Suppose that we examine such a roaring random signal passing through a bandpass filter that gets narrower and narrower, as in Figure 21.14.1.

 

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Figure 21.14.1 Concept of a spectral “slice”
“In examining 10 to 2,000 Hz, what would we find? Nowhere would we find a sinusoid, as in Figure 21.13.1”

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Figure 21.13.1 Several constant amplitude sinusoids

“Figure 21.13.2 is a more accurate representation of what we would find. It shows moment-by-moment variations, unpredictable variations in amplitude, of a signal found in a narrow frequency “slice” of a broadband random vibration. Unpredictable variations are what we mean by random. Broad-spectrum random vibration contains not sinusoids but rather a continuum of vibrations. Examining (in the time domain) a “slice” of that broad-spectrum random vibration gives us Figure 21.13.2.” In short, the amplitudes are unpredictable but the frequencies are known.

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Figure 21.13.2 Narrow-band response

“Am I sure of this?” Joe asks. “No, I’m not. But I’m trying to answer your question.”

Next week what?
“Let’s on our final two Monday mornings discuss the random vibration testing that you folks wanted to hear about. How did we at one time and how does Joe currently vibrate customer hardware to a random vibration spectrum such as this one?”

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Figure 22.5.1 Typical random vibration test spectrum

What is author Wayne Tustin doing these days? Well, November 4-6 he’ll be teaching about random vibration and shock testing at NTS in Huntsville, Alabama. On some previous Huntsville visits, Wayne’s “open course” host was called Wyle Laboratories. On other visits, NASA or the Army had contracted for “closed” courses at Redstone Arsenal.