Movable Rigid Scatterer Model for Flexural Wave Scattering on Thin Plates

Rigid scatterers are fundamentally important in the study of scattering of many types of waves. However, in the recent literature on scattering of flexural waves on thin plates, a “rigid scatterer” has been used to represent a clamped boundary. Such a model physically resembles riveting the plate to a fixed structure. In this paper, a movable model for a rigid scatterer that allows rigid-body motion is established. It is shown that, when the mass density of the movable rigid scatterer is much greater than that of the host plate and at high frequencies, the movable rigid scatterer approaches the limiting case that is the riveted rigid scatterer. The single- and multiple-scattering by such scatterers are examined. Numerical examples show that, at the extreme end of lower frequencies, the scattering cross section for the movable model vanishes while that of the riveted models approaches infinity. An array of such movable rigid scatterers can form a broad and well-defined stop band for flexural wave transmission. With a volume fraction above 50%, the spectrum is rather clean: consisting of only an extremely broad stop band and two groups of higher frequency Perot–Fabry resonance peaks. Increasing either scatterer’s mass density or the lattice spacing can compress the spectral features toward lower frequencies.

Flexural Wave Scattering by Double Elliptic Holes in an Infinite Thin Plate

In mechanical engineering and aerospace engineering, thin plate structure is used widely. For the sake of fixing bolt, it often design open holes in the plate. Sometimes elliptic holes should be used inevitably. When the plate is overloaded or the load is changed regularly, flexural wave is propagating in the plate. Because there are holes, it can cause stress concentration. Stress concentration could decrease the bearing capacity of structure, and reduce the service life of structure. The problem of flexural wave scattering by holes in the plate is one of the important and interesting questions in aerospace engineering for the latest decades. There are lots of materials obtained by theoretical research and experimental investigation. The problem is complicated, because there are many factors influenced. It is hard to obtain analytic solutions except for several simple conditions. In this paper, based on the theory of elastic thin plate, by using wave function expansion method and multi local complex coordinates, scattering of flexural wave and dynamic stress concentration by double elliptic holes in the thin plate are investigated. In the complex plane, the displacement field aroused by incident wave and the scattering displacement field impacted by double elliptic holes comprised of Fourier-Bessel series with undetermined coefficients are constructed. Through applying the method of multi local complex coordinates, the equations with unknown coefficients can be obtained by using the stress-free condition of the double elliptic holes in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. So the analytical solution of this problem is obtained. By using the displacement and stress expressions, an example is provided to show the effect of the change of relative location of the elliptic holes.

Characterization of Delamination in Beams Using Flexural Wave Scattering Analysis

An analytical model for the characterization of delamination in beams using flexural wave scattering analysis is presented. In the beam model of wave propagation, the beam is divided into four regions; to each of them the beam theory of wave propagation is applied to obtain the wave fields excited by a harmonic load on the beam surface. The solution for the entire beam is obtained in terms of the solution for the respective regions using continuity conditions at the junctions. Numerical results on beam displacement for various delamination sizes, materials and excitation frequencies are presented. Experiments using a scanning laser vibrometer on specimens containing simulated delamination are also conducted. The results are then verified by comparing with those obtained by the Strip Element Method (SEM) and experiment. Good agreement is observed between the present model with SEM and experiment.