"Cumulative effect" of second harmonic Lamb waves in a lossy plate

The second harmonic Lamb waves have high sensitivity to microstructural defects in materials and are therefore promising for incipient damage detection and monitoring of thin-walled structures. Existing studies have shown that the second harmonic Lamb waves can be cumulative with increasing propagation distance under the internal resonance conditions, which is conducive to nonlinear wave measurements in view of structural health monitoring. However, when propagating in a lossy structure with damping, the cumulative properties of the second harmonic Lamb waves are affected by energy dissipation and thus need to be re-examined. In this paper, a method for predicting the cumulative characteristics of second harmonic Lamb waves in damped plates is proposed. Instead of using material damping parameters which are difficult to obtain in practice, the proposed method relies on the attenuation patterns of Lamb waves at fundamental and double frequencies while taking into account the influence of the wave beam divergence. The proposed methodology is validated by finite element simulations and experiments. The results show that the cumulative second harmonic Lamb waves in the damped plate tend to increase and then decrease, and a "sweet" zone of relatively large amplitude can be predicted using the proposed method. The elucidation of the cumulative characteristics of the second harmonic Lamb waves provides guidance for effective system design for structural damage detection and monitoring applications.