Abstract
In this study, the reciprocity theorem for elastodynamics is transformed into integral representations, and the fundamental solutions of wave motion equations are obtained using Green’s function method that yields the integral expressions of sound beams of both bulk and Rayleigh waves. In addition to this, a novel surface integral expression for propagating Rayleigh waves generated by angle beam wedge transducers along the surface is developed. Simulation results show that the magnitudes of Rayleigh wave displacements predicted by this model are not dependent on the frequencies and sizes of transducers. Moreover, they are more numerically stable than those obtained by the 3-D Rayleigh wave model. This model is also applicable to calculation of Rayleigh wave beams under the wedge when sound sources are assumed to radiate waves in the forward direction. Because the proposed model takes into account the actual calculated sound sources under the wedge, it can be applied to Rayleigh wave transducers with different wedge geometries. This work provides an effective and general tool to calculate linear Rayleigh sound fields generated by angle beam wedge transducers.
Highlights
Rayleigh waves propagating on an elastic solid surface are commonly used in nondestructive testing and evaluation
This research presents a framework for analyzing and modeling the Rayleigh wave sound fields generated by angle beam wedge transducers
To make the integral region match with the actual Rayleigh sound sources area under the wedge, the conventional line integral representation has been extended to the surface integral expression using the algorithmic method
Summary
Rayleigh waves propagating on an elastic solid surface are commonly used in nondestructive testing and evaluation. Their method is based on the initial work by Aki and Richards,[18] in which, Rayleigh waves are assumed to propagate in a laterally homogeneous medium and the magnitudes of two horizontal components of Rayleigh waves are assumed to be dependent on the positions of the source and receiver.[19] This 3-D model was further developed by using the Fourier transform approach and simplified with a multi-Gaussian beam model.[20,21] this 3-D model addresses all of the above mentioned inadequacies, it still has some limitations It has difficulties predicting the correct magnitudes of Rayleigh sound beams, because the integral relation over an area with 2-D Green’s function does not match with reciprocal theorem for 2-D wave motions and will bring confused results, and the Fourier transform approach provides quite large magnitude values for displacements (the results for magnitudes of displacements solved by Fourier transform approach should be those for displacement potentials, and one can find this problem through the detailed derivation of Sec. 4 in the Ref. 13). IV provides the simulation results of Rayleigh sound fields and discusses specific advantages of the proposed method
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