Scattering of antiplane SH waves by fractal structures in strain gradient elasticity

Abstract Wave manipulation is essential in applications including seismic wave protection, sound isolation and acoustic device design. This study examines the scattering and trapping of antiplane shear horizontal (SH) waves in a microstructured solid embedded with rigid pins. The material’s response is governed by strain gradient elasticity. A method is proposed for identifying frequencies that induce resonance in the elastic body, based on specific material parameters and pin configurations. The analysis focuses on a system featuring a Koch snowflake-type pin layout, a fractal curve generated through an iterative process. This geometry allows exploration of a complex arrangement characterized by a high concentration of sharp corners that promote scattering. The system’s response to this self-similar configuration is analysed and compared to circular pin arrangements with an equivalent number of pins. A distinct resonance mode is identified, where motion is trapped within the pin configuration and the conditions for its emergence are analysed in detail. Furthermore, the study explores the influence of the characteristic lengths induced by dynamic gradient elasticity. The findings indicate that in fractal pin arrangements, the system’s response is dictated more by the fractal dimension than the number of pins, highlighting the significance of geometry in wave dynamics.