Wave propagation analysis for a second strain gradient rod theory

Guang Zhu (1) , Christophe Droz (1) , Abdelmalek Zine (2) , Mohamed Ichchou (1)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes
2 MMCS - Modélisation mathématique, calcul scientifique

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.

Mots clés: Dynamic behavior; Energy flow; Enriched rod model; Reflection and transmission; Second strain gradient theory; Wave propagation features

Domaines: Milieux fluides et réactifs; Acoustique [physics.class-ph]; Matériaux; Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Guang Zhu, Christophe Droz, Abdelmalek Zine, Mohamed Ichchou. Wave propagation analysis for a second strain gradient rod theory. Chinese Journal of Aeronautics, 2019, 33 (10), pp.2563-2574. ⟨10.1016/j.cja.2019.10.006⟩. ⟨hal-02712551⟩