Leveraging Fractal Geometries to Improve Structural Health Monitoring Systems

Abstract

Fractal geometries are characterized by interesting properties that have not yet been exploited for structural health monitoring (SHM). Among such properties, scale invari- ance and self-similarity are worth mentioning. We investigated whether using fractal geometry to develop sensors or self-sensing structures can enhance SHM performance. The latter solution brings about the possibility of integrated damage diagnosis by elimi- nating the need for external sensors. The theory of fractals was used, along with numerical simulations and experimental tests, to evaluate the feasibility of designing sensors and structures with fractal properties for enhanced SHM performance. In particular, a unique solution to develop a sensor or structural component based on the Sierpinski triangle was studied. Due to its hierar- chical structure, the considered fractal geometry inherently possesses frequency domain characteristics that make it highly sensitive to local variations across scales. Preliminary results brought evidence that fractals can be exploited to design highperformance SHM solutions, either as standalone fractal sensors or as self-sensing fractal structures. In addition, the efficient, lightweight, and multiscale nature of these systems makes them suitable for applications in several fields, including aerospace, mechanical, and biomedical engineering. This work contributes to the advancement of SHM technologies by introducing a new paradigm in sensor design and damage detection. The combination of fractals with engineering applications shows the feasibility of advancing engineering by integrating complex physics principles and has potential implications for a wide range of industries.