Scattering of Antiplane Shear Waves by Fractals in Strain Gradient Elasticity

TL;DR

This paper investigates how fractal geometries influence the scattering and resonance of antiplane shear waves in strain gradient elastic materials, revealing the dominant role of fractal dimension over pin count.

Contribution

It introduces a novel analysis of wave scattering in fractal pin arrangements within strain gradient elasticity, highlighting the impact of fractal geometry on wave trapping and resonance.

Findings

Fractal pin arrangements significantly affect wave scattering and resonance.

Resonance modes are primarily dictated by fractal dimension rather than pin number.

Self-similar fractal geometries enhance wave trapping compared to regular configurations.

Abstract

Wave manipulation is essential in various applications, including seismic wave protection, sound isolation, and acoustic device design. This study examines the scattering and trapping of antiplane SH waves in a microstructured solid embedded with rigid pins. The material's response is governed by the theory of strain gradient elasticity. A method is proposed for identifying the wavenumbers 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 the 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 the motion is trapped within the pin configuration and the conditions for its emergence are analyzed in detail. Furthermore, the study explores the influence of the characteristic lengths of the problem that are induced by the dynamic gradient elasticity theory. The findings indicate that in fractal pin arrangements, the system's response is rather dictated by the fractal dimension rather than by the total number of pins, highlighting the significance of geometry in wave propagation dynamics.