Modelling Low-Frequency Vibration and Defect Detection in Homogeneous Plate-Like Solids

Abstract

The inspection of thick-section sandwich structures with skins around core materials such as honeycomb, balsa, and foam relies on low-frequency vibration techniques to identify defects through changes in amplitude or phase response. However, current industrial methods are often limited to detecting specific types of defects, potentially overlooking others. Moreover, these methods do not gather detailed information about the defect type or depth, as they only analyse a small portion of the available data instead of the full relevant response spectrum. This paper explores the scientific basis of using low-frequency vibration in the pitch-catch variant for defect detection in homogeneous solids, through analysis of the full relevant frequency spectrum (5–50 kHz). Defects in structures lead to reduced local stiffness and mass in the affected area, causing resonance in the layer above, resulting in amplified vibrations known as local defect resonance (LDR). In this work, an aluminium plate with a 40 mm diameter circular flat-bottomed hole (FBH) at a depth of 1 mm (representing a skin defect) is excited with a chirp signal of 5–50 kHz, and the response is monitored 17 mm away from the excitation point. Finite-element analysis (FEA) is used for the numerical model, addressing challenges in creating an accurate model. The process to optimise the numerical model and the reduce model-experiment error is outlined, including challenges such as the lack of knowledge of material damping. The study emphasizes the importance of modelling the probe’s stiffness and damping effects for achieving agreement between the model and experiment. After incorporating these effects, the maximum LDR frequency error decreased from approximately 3 kHz to less than 1 kHz. In addition, this study presents a method with the potential for defect classification through comparison to modelled responses. The minimum difference error was used to quantify the resonance frequencies’ error between the model and the experiment. Since the resonant frequencies are a function of the defect’s shape, size, and depth, a relatively low root mean squared (RMS) error across the resonance frequency error spectrum indicates the defect’s characteristics. Finally, defect detection and sizing using the pitch-catch probe are explored with a wide-band excitation signal and a line scan through the mid-plane of the defect. A method for defect sizing using a pitch-catch probe is presented and experimentally validated. Accurate defect sizing is achieved with the pitch-catch probe when the defect width is at least ≥\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ge $$\\end{document} twice the 17 mm pin-spacing of the probe.