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.

译文

:关于由非线性声波在具有二次非线性的弹性固体中传播产生的准静态位移脉冲的形状,科学界尚无定论。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,其前沿的峰值位移与音调脉冲串的长度成正比。相反,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,其中峰值位移与传播距离成正比。这项研究提出了准静态位移脉冲的严格数学分析和数值模拟。在半无限固体的情况下,已确认由纵向平面波产生的准静态脉冲的时域形状不是直角三角形。对于有限尺寸的固体,不能简单地使用线性反射系数来建模样本的有限轴向尺寸,而线性反射系数会忽略入射场和反射场之间的非线性相互作用。更深刻地讲,与相同的换能器产生的基波和二阶谐波脉冲相比,有限孔径的换能器产生的准静态脉冲遭受更严重的发散。

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