Influence of planar cracks in plates on reflected and transmitted fields of Gaussian acoustic beams

Abstract

The scattering of a Gaussian beam by a rectangular crack is studied by means of the radiation mode model. The orthogonal set of modes for a L/S/V structure is derived, and a general mode decomposition formula is developed. The influence of a crack on the reflected and transmitted fields of a bounded beam, incident at critical angles of the L/S/L- and the L/S/V structure, is studied and physical interpretations are given. From those interpretations, the starting point of the crack is deduced along with the length and distance to the surface. Effects on focused beams are considered as well.

The radiation mode theory in ultrasonics

“…Later, a study was performed on inclusions near the surface [19], similar results also were found for that case.…”

“…The other two methods consist of giving the mathematics behind the theory with or without poetic explanations. The latter two methods can be found in the few papers [9]- [19] that already exist on the RMT and are automatically lengthy and cumbersome. For that reason we will deal with the first method, explaning the basics in words and running the risk of giving the misplaced impression that it is a simple theory.…”

“…Such boundary conditions are, for example, a Gaussian bounded beam incident on a given spot under a given angle. For a more detailed explanation of the basics of RMT, we kindly refer to [9]- [19]. In what follows, the term relative amplitude always means the amplitude of the particle displacement parallel to the solid-liquid interface (|u z |), divided by the incident amplitude.…”

“…In addition, there is also the inhomogeneous wave method [6], which is accompanied by severe numerical problems. The radiation mode theory (RMT), first created and applied in electromagnetism [7], [8] and later developed in acoustics [9]- [19], provides a physical and mathematical solution to such problems. In the RMT, no integration path is needed in the Cartesian axes system (x, y, z) but only in the phase space (k y ).…”

Lamb mode conversion in an absorptive bi-layer with a delamination

“…[3][4][5] Reflection and transmission of an incident Gaussian acoustic beam through the plate with a horizontal delamination immersed in a liquid was analyzed and a considerable influence of a delamination on the nonspecular lobe in the reflected beam was found. 9 The effect of mode conversion on a horizontal delamination in a thick multimode plate was theoretically studied and it was shown that, depending on a delamination length, a considerable part of an incident Lamb mode ͑or Rayleigh wave͒ energy can be converted into several transmitted Lamb modes. 10 It is necessary, however, to mention that all these papers were devoted to study Lamb modes interaction with a delamination located only in a simple homogeneous plate.…”