Computational characterization of the wave propagation behaviour of multi-stable periodic cellular materials

TL;DR

This paper computationally analyzes wave propagation in multi-stable periodic cellular materials, revealing their ability to exhibit tunable band gaps and energy dissipation through cell-level elastic instabilities, with implications for designing advanced wave control materials.

Contribution

It introduces a novel computational approach for analyzing wave behavior and band gap tuning in multi-stable cellular materials, combining dispersion analysis with structural deconstruction.

Findings

Materials exhibit low-frequency band gaps for small amplitude waves.

Modifying the unit cell geometry shifts the band gap positions.

The material behaves like a locally resonant system with tunable wave filtering.

Abstract

In this work, we present a computational analysis of the planar wave propagation behavior of a one-dimensional periodic multi-stable cellular material. Wave propagation in these materials is interesting because they combine the ability of periodic cellular materials to exhibit stop and pass bands with the ability to dissipate energy through cell-level elastic instabilities. Here, we use Bloch periodic boundary conditions to compute the dispersion curves and introduce a new approach for computing wide band directionality plots. Also, we deconstruct the wave propagation behavior of this material to identify the contributions from its various structural elements by progressively building the unit cell, structural element by element, from a simple, homogeneous, isotropic primitive. Direct integration time domain analyses of a representative volume element at a few salient frequencies in the stop and pass bands are used to confirm the existence of partial band gaps in the response of the cellular material. Insights gained from the above analyses are then used to explore modifications of the unit cell that allow the user to tune the band gaps in the response of the material. We show that this material behaves like a locally resonant material that exhibits low frequency band gaps for small amplitude planar waves. Moreover, modulating the geometry or material of the central bar in the unit cell provides a path to adjust the position of the band gaps in the material response.