The alternative Kirchhoff approximation in elastodynamics with applications in ultrasonic nondestructive testing

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. doi:10.1017/S1446181120000036

Contribution estimation of singular points in solving problems of radiation of HF VHF wire antennas arbitrarily located above the earth

The radiation solving the problem features of the wire antennas placed above the earth are considered. Based on the method of integral equations, the singular points contribution in solving radiation problems of the HF VHF wire antennas arbitrarily located above the earth is researched. The contribution of singular points is estimated depending on the frequency and parameters of the earth. It is shown that in the HF and VHF waves, their contribution of singular points is significant. The radiation solving the problem features of the wire antennas placed above the earth are considered. The value of elements of the Green’s tensor function is usually expressed in the Sommerfeld’s integrals form. The aim of this work is to estimate the contribution of singular points to the value of Sommerfeld’s integrals. Based on the method of integral equations, the singular points contribution in solving radiation problems of the HF VHF wire antennas arbitrarily located above the earth is researched. The contribution of singular points is estimated depending on the frequency and parameters of the earth. It is shown that in the HF and VHF waves, their contribution of singular points is significant.

THE ALTERNATIVE KIRCHHOFF APPROXIMATION IN ELASTODYNAMICS WITH APPLICATIONS IN ULTRASONIC NONDESTRUCTIVE TESTING

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.