Scattering of Flexural Waves From a Coated Cylindrical Anomaly in a Thin Plate

Scattering of flexural waves by a pit of quadratic profile inserted in an infinite thin plate

“…where the x axis is the reference axis for the angle θ and r is defined in Eq. (12). Substituting ( 16) into (3) and applying the orthogonality property of the functions cos(nθ) lead to the following equation satisfied by W int n ( r) for each circumferential order n : [13,20], Eq.…”

“…The same authors [11] also analyzed the same scatterers within the framework of the Mindlin plate theory and pointed out the difference between these two plate theories. V. A. Squire and T. W. Dixon [12] applied a similar method to analyze the flexural wave scattering from a coated cylindrical obstacle in an infinite thin plate. In this case, since the scatterer is penetrable, the coupling between internal and external displacement fields is described by the continuity relations at the interface.…”

Scattering of flexural wave in a thin plate with multiple circular holes by using the multipole Trefftz method

“…The complex variable function approach and conformal mapping technique were employed to solve the diffraction problem of flexural waves by two cutouts (Hu et al, 1998) and dynamic concentration factors of plates with two circular holes were presented under various boundary conditions. Squire and Dixon (2000) applied the wave function expansion method to study the scattering properties of a single coated cylindrical anomaly located in a thin plate on which flexural waves propagate. Gao et al (2001) dealt with theoretical and numerical analysis of scattering of elastic wave and dynamic stress 0020-7683/$ -see front matter Ó 2009 Elsevier Ltd. All rights reserved.…”

Ultrasonic Energy Transfer and Stress Concentrations in a Single-Fiber Composite with Absorbing Interface Layer

“…The latter author also proposed a novel method for analyzing the scattering by single cylindrical scatterers having internal delineative interfaces and used a simple two-layered scatterer subjected to SH-incident waves to illustrate the detailed solution procedure [3]. Squire and Dixon [13] examined the scattering properties of a single, coated cylindrical anomaly located in a thin plate on which flexural waves propagate using a series expansion of Bessel functions. Qin et al [14] analyzed three kinds of resonant modes of a single layered circular elastic cylinder embedded in the elastic medium for an incident longitudinal plane by considering the oscillation of the scatterer's core, based on the fact that the core moves as a rigid body when the shell material is very compliant.…”