The Kirchhoff approximation is widely used to describe the scatter of elastodynamic waves. It simulates the scattered field as the convolution of the free-space Green’s tensor with the geometrical elastodynamics approximation to the total field on the scatterer surface and, therefore, cannot be used to describe nongeometrical phenomena, such as head waves. The aim of this paper is to demonstrate that an alternative approximation, the convolution of the far-field asymptotics of the Lamb’s Green’s tensor with incident surface tractions, has no such limitation. This is done by simulating the scatter of a critical Gaussian beam of transverse motions from an infinite plane. The results are of interest in ultrasonic nondestructive testing.

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弹性动力学中的替代基尔霍夫近似在超声无损检测中的应用

基尔霍夫近似被广泛用于描述弹性动力波的散射。它将散射场模拟为自由空间格林张量与散射体表面上总场的几何弹性动力学近似的卷积，因此不能用于描述非几何现象，例如头波。本文的目的是证明另一种近似，即兰姆格林张量的远场渐近与入射表面牵引力的卷积，没有这样的限制。这是通过模拟横向运动的临界高斯光束从无限平面的散射来完成的。结果在超声波无损检测中很有意义。