Low frequency elastic wave propagation in 2D locally resonant phononic crystal with asymmetric resonator

TL;DR

This paper investigates low-frequency elastic wave behavior in a 2D phononic crystal with asymmetric elliptic resonators, revealing resonance modes that control wave transmission and reflection, including a mode enabling total transmission at specific frequencies.

Contribution

It introduces a semi-analytic method to analyze resonance modes in asymmetric elliptic resonators within phononic crystals, highlighting a mode that achieves total wave transmission due to zero effective mass density.

Findings

Resonance modes cause wave reflection and transmission effects.

A mode with zero effective mass density enables total wave transmission.

Resonance frequency varies with the elliptic resonator's orientation.

Abstract

The resonance modes and the related effects to the transmission of elastic waves in a two dimensional phononic crystal formed by periodic arrangements of a two blocks unit cell in one direction are studied. The unit cell consists of two asymmetric elliptic cylinders coated with silicon rubber and embedded in a rigid matrix. The modes are obtained by the semi-analytic method in the least square collocation scheme and confirmed by the finite element method simulations. Two resonance modes, corresponding to the vibration of the cylinder along the long and short axes, give rise to resonance reflections of elastic waves. One mode in between the two modes, related to the opposite vibration of the two cylinders in the unit cell in the direction along the layer, results in the total transmission of elastic waves due to zero effective mass density at the frequency. The resonance frequency of this new mode changes continuously with the orientation angle of the elliptic resonator.