Sustained propagation on periodic structures

The material configuration that generates propagation phenomena tolerant of the most elementary mathematical formulation is illustrated by the sequence of point masses linked by elastic forces. These are repetitive cells containing mechanical resonators that lend themselves easily to the calculation of wave phenomena leading to some remarkable physical properties. As the model thus configured can also be applied to electrical resonators consisting of a series of quadrupoles, this first paragraph will be divided into two parts. The first contains the demonstrations leading to the concepts of cutoff pulsation, dispersion diagram and wave velocities propagated on a mechanical chain. The second extends these concepts to chains of electrical resonators, making extensive use of the equivalence principle linking physical mechanical parameters to physical electrical parameters.

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