As noted there using the results of performed experimental investigations Braille elements do not have substantial effect to the shape of the
eigenmodes. Because of this fact numerical investigations of vibrations of the elastic structure without Braille elements is performed.
In a real-life scenario, the vibration characteristics (eigenvalues and
eigenmodes) of the real damaged structure would have to be determined (measured) by experiment.
Five
eigenmodes were observed, and the frequency ranged from 0.3 GHz to 3 GHz.
Equation (15) gives the general form of the
eigenmode of the plate in the x-direction.
The DD's are obtained by solving the
eigenmode equation associated to the unit cell geometry considering appropriate periodic boundary conditions in both Cartesian directions.
The resulting
eigenmode W(s) is approximately constant, with [n.sup.2] = [R.sup.2.sub.M]/[r.sup.2.sub.m]; as in Rayleigh's analysis.
Accordingly, the condensed structure can be obtained by the n
eigenmode of whole structure starting from low order, which is described in the following equation.
For a given [sigma] > 0, the smallest eigenvalue [[chi].sub.1]([sigma]) and corresponding eigenfunction [u.sub.1] define the
eigenmode which is called the fundamental mode (see the bottom curve plotted by the red solid line in Figure 2).
As the tuning of the two resonances by a single geometric parameter l (the length of the strip) is not feasible, the
eigenmode overlap is obtained by adjusting either the spacer or the alignment of the paired metallic strips [20].
The high-frequency characteristics of the double-slotted helix SWS, which include dispersion characteristics, interaction impedance, are calculated by the
eigenmode solver with master and slave boundary conditions [23] in the 3-D electromagnetic simulation software Ansoft HFSS [24].