# Mechanical vibration of objects

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 $j^2 = -1$.

• Would FEM combined with spectral decomposition work for you? – fibonatic Feb 14 '18 at 14:23
• Try one of Meirovitch's textbooks – Daniel K Feb 17 '18 at 23:57
• 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. – Tony Stewart Sunnyskyguy EE75 Apr 25 '18 at 6:53