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Do you happen to know relevant references in the literature that model the mechanical vibrations of a solid object (preferably antennas) by means of complex representations as a function of time?, i.e. can we say that the radial displacement can be modeled as

$$ r(t) = \sum_{i=1}^{N}{a_i \exp\left(-j b t \cos(\phi_i)\right)}$$

where $a_i, b,$ and $\phi_i$ are constant independent of time $t$ and $j$ is the complex number such that $j^2 = -1$.

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    $\begingroup$ Would FEM combined with spectral decomposition work for you? $\endgroup$
    – fibonatic
    Commented Feb 14, 2018 at 14:23
  • $\begingroup$ Try one of Meirovitch's textbooks $\endgroup$
    – Daniel K
    Commented Feb 17, 2018 at 23:57
  • $\begingroup$ You can not generalize with all structural antenna for dampening Q , f and wind resistance , moment of inertia etc and this equation would vary according to what it needs to be for phase jitter. $\endgroup$ Commented Apr 25, 2018 at 6:53

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No, I didn't check but I don't think these type of equations would be in a mechanical vibrations textbook mainly because a forcing function or initial displacement is not present, nor is the distance from the base of the antenna. In addition to mechanical vibrations equations, Finite element analysis can provide radial displacement. Textbooks links are below:

https://www.amazon.com/Mechanical-Vibrations-6th-Singiresu-Rao/dp/013436130X/ref=sr_1_1?ie=UTF8&qid=1519437095&sr=8-1&keywords=mechanical+vibrations

https://www.amazon.com/Schaums-Outline-Mechanical-Vibrations-Graham/dp/0070340412/ref=sr_1_6?ie=UTF8&qid=1519437095&sr=8-6&keywords=mechanical+vibrations

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  • $\begingroup$ Is it possible to cite references where I can find the model you're talking about. Thanks. $\endgroup$
    – Jeremy
    Commented Feb 18, 2018 at 5:11

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