Scattering Of Rough Surfaces And Elastic Guided Waves In Rough Plates

Two elastic wave problems related with the rough surface, scattering of elastic waves by a rough free surface and the propagation of elastic waves in a plate with rough surfaces, are studied in this paper. The rough surface problems are important in various physical situations, such as the quality detection of the devices with rough surfaces, detection of flaws with rough surfaces. The rough surface problems have been studied in the Electromagnetic, Optics and Ocean Acoustic. However, much less have been done in the area of the elastic wave. Our analysis is based on the concept of scattering amplitude (SA) which is the amplitude of scattering plane wave. SA method is very convenient for the rough surface problem. In solid media, there are two kinds of waves-P wave and S wave-and they are coupled at the surface, making the scattering problem in solid media more difficult than that of the scalar wave. The incident wave, reflected wave, boundary equation and scattering amplitude are expressed by matrix, which simplified the analyzing and computing process.After a review of different methods available for the rough surface, we choose the small perturbation approximation to expand the wave field, SA and boundary equation in the power of rough elevation. By solving the boundary equation, we get the first and second order of scattering amplitude. The general result is used for an example—the scattering problem of the rough surfaces with Gaussian distribution. The mean field and variance are given. At last, SA matrixes under different cases are computed, and the results are compared with that got by phase screen approximation.The characters of Lamb wave propagating in solid plate with rough surfaces are studied on the basis of scattering of rough surfaces. We get Rayleigh-Lamb frequency equation expressed with SA matrix by introducing the noncorrelated successive reflection approximation. There are some differences for the Rayleigh-Lamb frequency equation of compared with that of the plane surfaces. Through these differences we get a small perturbation Δk on wave vector k. The...