An insight on local defect resonance based on modal decomposition analysis: A two-dimensional case

Abstract

The resonance behaviors of defects, specifically local defect resonance (LDR), are useful for defect detection in structures. However, there is a lack of intuitive elucidation regarding the underlying mechanisms governing defect resonance. This study aims to analyze the LDR of a horizontal crack in a plate activated by Lamb waves using the modal decomposition method (MDM). The MDM involves an approximate decomposition of the wavefield into finite constituent Lamb wave modes, including propagating, non-propagating, and inhomogeneous modes. The amplitude of each mode is determined according to the continuous boundary conditions of displacement and stress between the damaged zone and the intact zone. Analytical results reveal specific frequencies at which the damaged zone exhibits significantly stronger vibrations than the intact zone, indicating the emergence of LDR. The corresponding wavefields exhibit various resonance patterns, encompassing both in-plane LDR and out-of-plane LDR types. In contrast to finite element simulations and experimental observations, the MDM unveils the dominant constituents of resonance patterns: out-of-plane LDR results from the combination of reflected and transmitted A0 and A1 modes within the damaged zone, while in-plane LDR is formed by the superposition of reflected and transmitted A0, A1, and S0 modes.