Energy Distribution and Exchange Between Spatial Harmonics in Bending Wave Phononic Crystals

Abstract

Designing mechanical metamaterials is key to $e.g.$ vibration mitigation, wave guiding, lensing, and cloaking, and is mostly based on modeling a single unit cell of an infinite periodic assembly. The resulting dispersion relation is limited to wavelengths longer than the unit cell, but spatial harmonics should arise as well. Using iterative enhancement of inhomogeneous wave correlation, this study predicts and experimentally validates the distribution of energy between wave modes at a given frequency. In $b\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}d\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}g$ $w\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}e$ $b\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}d$ $g\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}s$, energy is seen to shift from bending waves to longitudinal waves.