Identifying elastic wave polarization and bandgaps in periodic solid media

No Thumbnail Available
Authors
Carrillo-Munoz, Maria J.
Sharma, Bhisham N.
Advisors
Issue Date
2023-08-15
Type
Article
Keywords
Research Projects
Organizational Units
Journal Issue
Citation
Carrillo-Munoz, M., & Sharma, B. (2023). Identifying elastic wave polarization and bandgaps in periodic solid media. International Journal of Mechanical Sciences, 252, 108363. https://doi.org/https://doi.org/10.1016/j.ijmecsci.2023.108363
Abstract

We present a new computational method to accurately identify the elastic wave propagation modes and polarizations in periodic solid structures and metamaterials. The method uses the eigenvectors associated with each propagating wave solution to calculate the contribution of each translational and rotational component of the total mass-in-motion. We use this information to identify the dominant wave propagation mode by defining a relative effective modal mass vector. Then, we associate each wave solution with its correct polarization by defining a polarization factor that quantifies the relative orientation between the wave propagation and lattice motion directions and provides a positive numerical value between 0 (pure S-wave) and 1 (pure P-wave). Further, we suggest a graphical representational scheme for easier visualization of the wave polarization within traditional dispersion plots. To validate the method, we compare our predictions against previously published results for various elastodynamic problems. Finally, we use the proposed method to analyze the effect of various lattice and structural parameter perturbations on the elastic wave propagation and polarized bandgap behavior of a square planar beam lattice. Our analysis reveals the emergence of previously unobserved dynamic characteristics, including various polarized bandgaps, fluid-like behavior, and ultralow-frequency SH- and SV-bandgaps that extend to 0 Hz. Our proposed method provides an alternative computational approach to the typically employed visual mode inspection technique and provides a robust method for analyzing the elastic wave response of periodic solid media.

Table of Contents
Description
Click on the DOI to access this article (may not be free).
Publisher
Elsevier Ltd
Journal
Book Title
Series
International Journal of Mechanical Sciences
Volume 252
PubMed ID
DOI
ISSN
0020-7403
EISSN