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I have a scenario where a spaceship has been badly damaged and now the normal vibrations of the power supply are becoming amplified through the damaged hull, and threatening to tear the ship apart.

Here comes the question part. If the vibrations are reflecting internally within the structure and creating interference patterns, could the actual molecular structure of the material itself be weakened?

(I have been thinking of using steel, but can switch to different materials if needed.)

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    $\begingroup$ Are you looking for something like aeroelastic flutter? It tore apart Braniff Flight 542. $\endgroup$ – HDE 226868 Jan 2 at 23:55
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    $\begingroup$ Hello Ken. Please help us out by explaining what effect you're trying to achieve. Disrupting a molecular structure is not what happens when you (e.g.) tear a piece of paper in half. It is what you get when you burn the paper. Vibration can break a weld, shear a bolt, tear metal, etc. But to really help you out, we need to better understand what you're trying to do with the answer. Thanks! $\endgroup$ – JBH Jan 3 at 0:14
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    $\begingroup$ yes, that's the presupposition. harmonic resonance provides positive feedback which amplifies the vibration. Obviously this can weaken the structure by placing forces beyond the designed parameters. That can loosen joints etc. The actual question though is - can it weaken the actual material itself? Maybe its a moot point as it is not necessary to do so, but just fact checking a very specific part of my description $\endgroup$ – ken Jan 3 at 0:16
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    $\begingroup$ I'm really just trying to wreck the ship, which is obviously possible. After a long paragraph describing the vibrations etc, I want to end it with this snippet. Does it work? $\endgroup$ – ken Jan 3 at 0:19
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    $\begingroup$ This massive structure was now being played from both ends, like a giant tuning fork, with positive feedback amplifying the vibrations to levels that the ship was not designed for. Even worse, these sympathetic vibrations were drifting in and out of phase slightly as the severed neck of the ship flapped slowly but uncontrollably. The phase discrepancies reverberated through the steel and bounced back toward each other, meeting in the central spans with cyclical flurries of chaotic and violent interference patterns, weakening the structural material at the molecular level. $\endgroup$ – ken Jan 3 at 0:19
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Short Answer is Yes, as this scientific paper describes. I suspect however your real question is why, and the answer for that is that right now, we don't have a complete enough picture of materials science to know with any certainty.

That said (and I make these statements with the caveat that I'm not a materials scientist), on many different scales, we see this all the time. On the planetary scale, we see IO being stretched and its shape deformed by the gravitational forces around Jupiter, and the volcanic activity formed by that movement. Bending a small length of metal back and forth quickly often makes it warm in the middle and more subject to failure, so we know that kinetic energy does have an impact on metals and many other materials in the manner you describe.

As for the specific vibration frequency that would cause the most impactful damage to your spaceship, you need to look at resonant frequencies. There are a few interesting mythbuster episodes where they try to collapse a bridge or explore earthquake machines by exploiting this concept. Certainly from a physics perspective, these terms, if used correctly, would at the very least add plausibility to your scenario.

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    $\begingroup$ "these terms, if used correctly" very much this. Just note that these terms, when used incorrectly, have exactly opposite effect. Sometimes it is better to write from layman perspective, then any inaccuracies can be blamed on fictional character and don't disturb suspension of disbelief that much, if at all. $\endgroup$ – Mołot Jan 3 at 9:25
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    $\begingroup$ Agreed - I shudder any time there's any serious depth of discussion of computer technology in fiction, and the oil drilling practices in "Armageddon" pretty much ruined the movie for me. $\endgroup$ – pojo-guy Jan 3 at 18:42
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Perhaps the spaceship was assembled with a thixotropic adhesive.

A thixotropic fluid is painted onto the various ship structural components and is ordinarily completely solid and inert (you don't even know it's there). However if you apply a very specific high energy frequency to the fluid (or the object that it resides on) its viscosity temporarily changes allowing it to flow onto other surfaces. Remove the frequency and the fluid reverts to it's default inert state thus binding two or more objects. The benefit is that the bond extends across the entire connecting surfaces between the objects (instead of just a single weld, bolt, rivet, etc) also the bond is completely reversible for disassembly and/or adjustment.

The down side is that if the same frequency is uncontrollably introduced (such as the resonance of a power supply against a damaged hull) the bonds will weaken thus compromising the integrity of the entire ship.

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