Description of bandgaps opening in chiral phononic crystals by analogy with Thomson scattering

Abstract

Chiral phononic crystals provide unique properties not offered by conventional metamaterial based on classic Bragg scattering and local resonance. However, it is insufficient to only consider the inertial amplification effect to describe its bandgap mechanism due to the absence of the bandgap caused by the chirality in some specific chiral structures. Here, we theoretically and experimentally introduce an analogy with Thomson scattering in electromagnetic waves to characterize the bandgap phenomena in chiral phononic crystals with translation-rotation coupling. Another phononic structures with translation-translation coupling are proposed to illustrate the universality of the analogy. We evidence that the coupling motion in chiral unit cells is similar to the result of Thomson scattering, which quantitatively formulizing as inertial amplification in theory and, twice elastic Thomson scattering allows the waves in the same polarization mode to superpose in antiphase, which is essence of the bandgap formation. This finding sheds a new light on the physics of the elastodynamic wave manipulation in chiral phononic crystals, thus opening a definite route for the pragmatic exploitation of chiral phononic crystals as well as other structures with motion coupling in achieving low-frequency and broad bandgaps.

Isotacticity in chiral phononic crystals for low-frequency bandgap

“…for this bandgap formation. This indirectly demonstrates that the analogous Thomson scattering [58] has universality.…”

“…According to the conditions of elastic Thomson scattering [58], ISL and SYL have to own translationrotation coupling. It has been demonstrated that the chirality is an effective way to achieve the motioncoupling condition, thus producing the inertial amplification effect [59,61].…”

“…In recent years, the inertial amplification was demonstrated in the axis twist metamaterials as well [56,57]. Subsequently, an analogue of Thomson scattering was proposed theoretically, numerically, and experimentally to describe its underlying physics [58]. From the physics point of view, the coupling of orthogonal polarizations is a means to amplify the inertia [56,57,59], while the destructive interference is another key factor in opening the bandgap [58].…”

“…Subsequently, an analogue of Thomson scattering was proposed theoretically, numerically, and experimentally to describe its underlying physics [58]. From the physics point of view, the coupling of orthogonal polarizations is a means to amplify the inertia [56,57,59], while the destructive interference is another key factor in opening the bandgap [58]. Achieving destructive interference relies on secondary scattered waves of the same polarization having opposite motion directions [58].…”

“…In fact, according to the three conditions for the bandgap generation [58], it is possible to achieve this bandgap even if the adjacent atoms in this non-mirror chiral lattice do not have alternating arrangement directions (isotacticity) as long as the horizontal tangential motion of the planar non-mirror chiral lattice (three-triplet lattice) is suppressed. Since the ligaments between adjacent lumped masses are continuous, theoretically, the number of wave reflections can be effectively reduced, which in turn reduces the resonance peaks in the FRF.…”