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

• Published in: European journal of mechanics, A, Solids Vol. 90; p. 104326
• Main Authors: Zhu, Guang, Zine, Abdelmalek, Droz, Christophe, Ichchou, Mohamed
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Masson SAS 01.11.2021; Elsevier BV; Elsevier
• Subjects: Acoustics; Analysis of PDEs; Complex media; Continuum mechanics; Coupling; Elastic waveguide; Energy transmission; Engineering Sciences; Functional Analysis; Heterogeneity; Mathematics; Mechanics; Numerical Analysis; S matrix theory; Scale models; Second strain gradient theory; Strain; Transmission coefficient; Transmitted energy; Vibration; Wave reflection; Wave scattering; Waveguides; Transmitted energy; Transmission coefficient; Second strain gradient theory; Complex media; Elastic waveguide; Wave scattering; wave scattering; elastic waveguide; complex media; transmission coefficient; transmitted energy
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2021.104326

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. •Proposing Second Strain Gradient theory-based wave scattering matrix method.•Introduce non-local coupling into a classical theory-based waveguide structure.•Physical interpretation of long-range interactions in non-local coupling region.•Influence of local behavior on wave transmission and conversion property.•Application in vibration isolation for engineering waveguide structures.