Fractal Analysis of Vibration Signals for Assessing Mechanical Material Properties Under Different Impact Forces

Abstract

 Understanding the mechanical properties of materials is essential in science and engineering to enhance product durability, safety, and performance, and to prevent structural failures. This study applies fractal analysis to investigate vibration signals  recorded by piezo film sensors during impact testing on four square-shaped materials: brass, copper, mild steel, and stainless steel. Using an impact hammer, each material was subjected to impact forces ranging from 300N to 800N. Vibration data was captured and analyzed in MATLAB using a box-counting algorithm to calculate fractal dimensions. The findings revealed a notable correlation between the calculated fractal dimensions and two critical mechanical properties, Poisson’s ratio and Young’s modulus. The fractal dimension is inversely ordered relative to the Poisson’s ratio values of the materials, while the order of the fractal dimension aligns with the order of Young’s modulus values. This suggests that materials with higher Young’s modulus values also display higher fractal dimensions, whereas materials with higher Poissons ratios exhibit lower fractal dimensions. These insights indicate that fractal analysis of vibration signals provides a reliable,
efficient, and cost-effective alternative to conventional methods for evaluating material properties. This approach holds significant potential for non-destructive testing applications, especially in fields requiring rapid and economical material assessments, such as aerospace, automotive, and construction.