Wave propagation analysis for a second strain gradient rod theory
Abstract
In this work, an enriched model describing the longitudinal wave propagation is established based on Mindlin's Second Strain Gradient (SSG) theory, which can describe the heterogeneity caused by the micro-structure interactions in the frame of continuum mechanics. The governing equation and associated boundary conditions are derived based on Hamilton's principle, then the dispersion relation of non-classical longitudinal wave together with the extra-waves appearing exclusively in SSG theory model are investigated. The investigations are based on the modal density, energy flow, and forced response of the rod. Wave transmission and reflection through planar interfaces based on the proposed model have been calculated. Finally, the results of the enriched model are well interpreted by comparing with the classical theory results, and some useful conclusions are derived on the SSG theory based model in the wave propagation characterization.
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BibTeX
@misc{zhu2026wave,
title = {{Wave propagation analysis for a second strain gradient rod theory}},
author = {Guang Zhu and Christophe Droz and Abdelmalek Zine and Mohamed Ichchou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33083},
eprint = {2610.33083},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33083},
}
RIS
TY - UNPB
TI - Wave propagation analysis for a second strain gradient rod theory
AU - Guang Zhu
AU - Christophe Droz
AU - Abdelmalek Zine
AU - Mohamed Ichchou
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.33083
UR - https://arxiv.org/abs/2610.33083
AB - In this work, an enriched model describing the longitudinal wave propagation is established based on Mindlin's Second Strain Gradient (SSG) theory, which can describe the heterogeneity caused by the micro-structure interactions in the frame of continuum mechanics. The governing equation and associated boundary conditions are derived based on Hamilton's principle, then the dispersion relation of non-classical longitudinal wave together with the extra-waves appearing exclusively in SSG theory model are investigated. The investigations are based on the modal density, energy flow, and forced response of the rod. Wave transmission and reflection through planar interfaces based on the proposed model have been calculated. Finally, the results of the enriched model are well interpreted by comparing with the classical theory results, and some useful conclusions are derived on the SSG theory based model in the wave propagation characterization.
ER -