School of Aerospace Systems, University of Cincinnati, Cincinnati, Ohio 45221, USA.
J Acoust Soc Am. 2013 Sep;134(3):1760-74. doi: 10.1121/1.4817840.
There is an unresolved debate in the scientific community about the shape of the quasistatic displacement pulse produced by nonlinear acoustic wave propagation in an elastic solid with quadratic nonlinearity. Early analytical and experimental studies suggested that the quasistatic pulse exhibits a right-triangular shape with the peak displacement of the leading edge being proportional to the length of the tone burst. In contrast, more recent theoretical, analytical, numerical, and experimental studies suggested that the quasistatic displacement pulse has a flat-top shape where the peak displacement is proportional to the propagation distance. This study presents rigorous mathematical analyses and numerical simulations of the quasistatic displacement pulse. In the case of semi-infinite solids, it is confirmed that the time-domain shape of the quasistatic pulse generated by a longitudinal plane wave is not a right-angle triangle. In the case of finite-size solids, the finite axial dimension of the specimen cannot simply be modeled with a linear reflection coefficient that neglects the nonlinear interaction between the combined incident and reflected fields. More profoundly, the quasistatic pulse generated by a transducer of finite aperture suffers more severe divergence than both the fundamental and second order harmonic pulses generated by the same transducer.
科学界对于具有二次非线性的弹性固体中非线性声波传播产生的准静态位移脉冲的形状存在悬而未决的争议。早期的分析和实验研究表明，准静态脉冲呈现出直角三角形的形状，前沿的峰值位移与音脉冲的长度成正比。相比之下，最近的理论、分析、数值和实验研究表明，准静态位移脉冲具有平顶形状，峰值位移与传播距离成正比。本研究对准静态位移脉冲进行了严格的数学分析和数值模拟。在半无限大固体的情况下，证实了由纵平面波产生的准静态脉冲的时域形状不是直角三角形。在有限尺寸固体的情况下，不能简单地用忽略组合入射场和反射场之间的非线性相互作用的线性反射系数来模拟样品的有限轴向尺寸。更重要的是，与同一换能器产生的基波脉冲和二次谐波脉冲相比，具有有限孔径的换能器产生的准静态脉冲的发散更为严重。
