非线性兰姆波在厚度缓慢变化和衰减下的特性分析

该文运用解析的方式推导了考虑声波衰减时兰姆波二次谐波的累积和传播规律，并用半解析方式将该理论推广到缓慢变厚度板的情况。由于色散特性，兰姆波二次谐波和基频波相速度不匹配，传播通常会产生拍频效应，使得二次谐波的振幅沿着传播距离周期性的归零。当考虑声波衰减或板的厚度缓慢变化的情况时，拍频效应将不再严格地被满足。二次谐波的振幅依然会沿着传播距离而振荡，但不会归零。该研究可以用于分析如何高效地激发和接收兰姆波的二次谐波，表征和评估不同厚度变化的结构中的微观结构损伤。

Characteristics of nonlinear Lamb waves with slowly-varying thickness and attenuation

In this paper, the accumulation and propagation of the second harmonics of Lamb waves under attenuation are derived analytically, and the theory is extended to the case of plates with slowly-varying thickness by semi-analytical method. Due to the dispersion characteristics, the phase velocity of the second harmonic wave and the fundamental wave do not match, and the propagation usually produces beat effect, making the amplitude of the second harmonic wave periodically zero along the propagation distance. The beat effect is no longer strictly satisfied when the acoustic attenuation or the slow change in the thickness of the plate are considered. The amplitudes of the second harmonic wave will still oscillate along the distance, but will not return to zero. This study can be used to analyze the conditions for efficient excitation and reception of Lamb wave second harmonics, and to characterize and evaluate microstructure damage in structures with different thickness variations.