Morlock Merlin B, Kim Jin-Yeon, Jacobs Laurence J, Qu Jianmin
School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0355.
Department of Civil and Environmental Engineering, Northwestern University, Evanston, Illinois 60208-3109.
J Acoust Soc Am. 2015 Jan;137(1):281-92. doi: 10.1121/1.4904535.
The mixing of two co-directional, initially monochromatic Rayleigh surface waves in an isotropic, homogeneous, and nonlinear elastic solid is investigated using analytical, finite element method, and experimental approaches. The analytical investigations show that while the horizontal velocity component can form a shock wave, the vertical velocity component can form a pulse independent of the specific ratios of the fundamental frequencies and amplitudes that are mixed. This analytical model is then used to simulate the development of the fundamentals, second harmonics, and the sum and difference frequency components over the propagation distance. The analytical model is further extended to include diffraction effects in the parabolic approximation. Finally, the frequency and amplitude ratios of the fundamentals are identified which provide maximum amplitudes of the second harmonics as well as of the sum and difference frequency components, to help guide effective material characterization; this approach should make it possible to measure the acoustic nonlinearity of a solid not only with the second harmonics, but also with the sum and difference frequency components. Results of the analytical investigations are then confirmed using the finite element method and the experimental feasibility of the proposed technique is validated for an aluminum specimen.
利用解析方法、有限元方法和实验方法，研究了在各向同性、均匀且非线性弹性固体中两个同向、初始单色瑞利表面波的混合情况。解析研究表明，虽然水平速度分量可以形成冲击波，但垂直速度分量可以形成一个脉冲，且与混合的基频和振幅的特定比值无关。然后，利用该解析模型来模拟基波、二次谐波以及和频与差频分量在传播距离上的发展情况。该解析模型进一步扩展，以包括抛物线近似中的衍射效应。最后，确定了基波的频率和振幅比，这些比值可提供二次谐波以及和频与差频分量的最大振幅，以帮助指导有效的材料表征；这种方法应该不仅能够利用二次谐波，还能利用和频与差频分量来测量固体的声学非线性。然后，使用有限元方法确认了解析研究的结果，并针对铝试样验证了所提出技术的实验可行性。
