French term (edited): modes propres de vibration

An oscillator's own modes of vibration (generally plural, as in the text) ARE its resonant frequencies (fundamental + harmonics), in the sense that the only characteristic of "mode" that you care about is its frequency.

What you want to avoid is having the irreducible vibration of the engine excite a resonant frequency of the airframe. That is why so much engineering goes into the engine mount.



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Note added at 15 hrs (2012-02-20 09:03:53 GMT)
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Or "eigenmodes of vibration", if you want to be fancy.:-)

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Note added at 12 days (2012-03-03 00:17:23 GMT) Post-grading
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As I noted, you could say “eigenmodes” of vibration if you wanted to be fancier. Contra Chris C., the term *most commonly* used in the STEM disciplines, by far, is “normal modes” of vibration/oscillation; prove this to yourself by comparing Google verbatim exact-phrase searches on the two terms coupled with “vibration” and/or “oscillation” for context. “Eigenmodes” comes a fairly distant second, and a longish list of others (proper, characteristic, etc.) come in behind. In a patent, “normal mode” may have the disadvantage in English of being a technical term that does not look like one.

The *notion* of own/proper/characteristic/natural/normal/simple/…/eigen- modes of vibration and resonant frequencies has existed at least since the Pythagoreans. Mathematicians in the 17th and 18th centuries devoted a lot of effort to explaining the phenomenon, and Daniel Bernoulli was the first to grasp the “permanence” of the “proper frequencies”. Leonhard Euler then outshone him by showing how to derive those frequencies from the equations of motion and publishing the first mathematical theory of the vibrations of a string (De vibratione chordarum, 1748). We know that Euler himself did not popularise the term “eigenmode” (if he even used it, which is doubtful) from the simple fact that almost all his treatises were published in Latin or French. For close to two centuries thereafter, the adjectives used to identify these modes in other languages were cognates or synonyms of proprius/propre or words like “natural” or “normal”, and by and large these variants still live today. (Google Ngram searches of books in the English corpus shows the frequency of “eigenmode” rising only after 1960 – and catching up with “proper mode”, in secular decline for two centuries, only around 2000.)

The recent spreading of “eigen” terms in English amounts to propagation by analogy of a concept, rather than a term, introduced by Euler, namely (what we now call) the eigenvector. The Wikipedia article on that term puts it nicely: “[where] an abstract direction is unchanged by a given linear transformation, the prefix ‘eigen’ is used, as in eigenfunction, eigenmode, eigenface, eigenstate, and eigenfrequency.”