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Transient Green's Tensor for a Layered Solid Half-Space With Different Interface Conditions



S C. Ren, Nelson N. Hsu, Donald G. Eitzen


Pulsed ultrasonic techniques can be and have been used to examine the interface conditions of a bonded structure. To provide a theoretical base for such testing techniques we model the structure as a layer on top of a half-space, both of different elastic properties, with various interface bonding conditions. The exact dynamic Green's tensor for such a structure is explicitly derived from three-dimensional equations of motion. The final solution is a series. Each term of the series corresponds to a successive arrival of a generalized ray and each is a definite line integral along a fixed path, which can be easily computed numerically. Willis' method is used in the derivation. A new scheme of automatic generation of the arrivals and ray paths using combinatorial analysis, and the summation of the corresponding products of reflection coefficients is presented. A FORTRAN code for computation of the Green's tensor when both the source and the detector are located on the top surface is developed. The Green's tensor is then used to simulate displacements due to pulsed ultrasonic point sources of known time waveform. Results show that the interface bonding conditions vary some of the first few head waves and regular reflected rays change polarities and amplitudes. This phenomenon can be sued to infer the quality of the interface bond of materials in ultrasonic nondestructive evaluation. In addition the results are useful in the study of acoustic microscopy probes, coatings, and geo-exploration.
Journal of Research (NIST JRES) -
107 No. 5


bond integrity, dynamic elasticity, fundamental solution, Green's function, interface condition, layered half-space, NDE theoretical mechanics, wave mechanics


Ren, S. , Hsu, N. and Eitzen, D. (2002), Transient Green's Tensor for a Layered Solid Half-Space With Different Interface Conditions, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed May 23, 2024)


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Created August 31, 2002, Updated October 12, 2021