Analysis of frequency gap of nanomechanical antenna structure resonator using mathieu equation

The frequency gap of an antenna structure resonator whose resonant frequency does not exist was already observed in the frequency range of 763 MHz ~ 1.197 GHz from calculated results using the Bernoulli-Euler equation. We could now obtain the frequency gap of 840 MHz ~ 1.197 GHz through derivation of the Mathieu equation under a reasonable approximation on the vibrating state of an antenna structure resonator with 20 elements on each side of a boom at a frequency of 1.49 GHz by applying the Bernoulli-Euler equation with the harmonic modulated outward axial force to the antenna structure resonator and then by setting the magnitude of the axial force to be 5.58×10^-5 N.