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 $j^2 = -1$.
