Wave transmission and reflection analysis through complex media based on the second strain gradient theory

Guang Zhu (1, 2) , Abdelmalek Zine (1, 3) , Christophe Droz (4) , Mohamed Ichchou (1, 2)

1 ECL - École Centrale de Lyon
2 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes
3 MMCS - Modélisation mathématique, calcul scientifique
4 KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven

The scattering of guided waves through a complex structure is of great importance in predicting vibration energy transmission and reflection across structures. Multi-scale models based on generalized continuum theory have been developed recently to investigate the vibration behavior of complex media in the frame of continuum mechanics. In this study, models based on the second strain gradient theory are employed together with a scattering matrix method to study the wave transmission and reflection through non-classical coupling regions between two waveguides. Numerical results are presented for longitudinal and bending waves through 1-D coupling interfaces. Upon which we discuss the local behavior of the internal heterogeneity in the complex coupling region and its impact on wave scattering properties at coupling interfaces. The results obtained also show that the proposed approach is of great potential in the investigation of vibration transmission control by enriching a waveguide's internal structure.

Mots clés: Second strain gradient theory; complex media; wave scattering; elastic waveguide; transmission coefficient; transmitted energy

Domaines: Mécanique [physics.med-ph]; Acoustique [physics.class-ph]; Analyse numérique [math.NA]; Analyse fonctionnelle [math.FA]; Equations aux dérivées partielles [math.AP]

Guang Zhu, Abdelmalek Zine, Christophe Droz, Mohamed Ichchou. Wave transmission and reflection analysis through complex media based on the second strain gradient theory. European Journal of Mechanics - A/Solids, 2021, 90, pp.104326. ⟨10.1016/j.euromechsol.2021.104326⟩. ⟨hal-03242745⟩