Certain equipment must be designed and tested to withstand external vibration excitation. This is common in the military, naval, aerospace and other industries.
The equipment is typically mounted on a shaker table and subjected to base excitation. The input may be random vibration if the field environment is likewise. In other cases, random vibration is used to verify the integrity of parts and workmanship separately from the maximum expected field environment.
The random vibration is typically specified as a power spectral density (PSD). Note that the workmanship screen and field level can be enveloped by a single PSD. A goal is to verify that the equipment operates properly before, during and after the random vibration test.
A more thorough test is to perform a sine sweep test before and after the random vibration test. A response accelerometer is mounted on the test article, in addition to the control accelerometer at the base input location. The objective is to determine whether any natural frequencies have shifted, or any other changes have occurred, as a result of the random test. Such changes could indicated loosened fasteners, crack formation or other defects.
A case history is given next. The data was sent to me by a colleague. I have requested further information on the equipment and will post a photo or diagram later if permission is granted.
A rocket engine assembly was subjected to a sine sweep test in conjunction with a random test. A resonant response occurred when the excitation frequency was swept through 85 to 86 Hz as shown in Figure 1. The equipment response would have had a similar frequency content to the input if it had been a well-behaved, linear, single-degree-of-freedom system. The response Fourier transform for the corresponding duration did have a spectral peak at 85.45 Hz matching the sweeping input frequency as shown in Figure 2.
(Note that this is an approximation because the Fourier transform is taken over a short duration and represents an average, whereas the input frequency has instantaneous change.)
But the response also showed integer harmonics with the highest peak at 683.6 Hz, which was 8x the fundamental frequency.
Please let me know if you have observed similar effects or have other insights. Hopefully, I can post more details later…
Sine Sweep Time History Data
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My colleague Albert Turk sent me a reply, paraphrased as follows:
I suspect a component with a resonance at the input frequency that is excited to the point of metal-to-metal impact. I have seen data from repetitive impact machines (HASS) and also from gunfire (50 cps) that had these integer multiples.
If so, the sinusoidal excitation has turned the assembly into a repetitive impact machine near 85 Hz. It would be interesting to see if there is a sine input amplitude threshold below which this suddenly goes away.
And Steve Zeise wrote:
I have observed this phenomenon and tracked it down to loose joints introducing impacts into the system.
Note that joints can slip under shock & vibration loads.
“Loss of clearance” of “loss of sway space” may be appropriate, related terms to describe the problem shown in the data. Further investigation is needed.