Surface Waves In Layered Half-Space-An Improved Laguerre Polynomial Approach

In the seismic exploration,geotechnical engineering,the nondestructive examination and fabrication of Acoustic Surface Wave devices,the situations of stratified half-space are often encountered,such as aquifer,oil,gas,highway pavement,foundation and surface acoustic wave sensors and the like.To a certain extent,these objects can be regarded as a stratified half-space consisting of homogeneous layered media.The study of the structural model has important theoretical guiding significance for engineering design.Functionally gradient materials(FGMs)are generally composed of two or more components.The volume content of each component varies continuously in space,which results in the material parameters are continuous functions of spatial position coordinates.The unique composition of FGM enables it to have excellent performance in thermal shock resistance,cracking resistance and fracture resistance,so it is gradually applied in the fields of machinery,electronics,optics,nuclear energy,chemistry,biomedicine and civil engineering.Ultrasonic technology is a very promising technique for the inspection of FGM.The effective use of ultrasonic for such a purpose depends on a good understanding of wave propagation in FGM.The conventional Laguerre polynomial approach can ensure that the displacement,electric potential and magnetic potential are continuous in the whole structure when dealing with the surface wave propagation in stratified half-space.However,for two adjacent layers with different material parameters,discontinuous stress,electrical displacement and magnetic induction intensity distribution will be generated.In order to overcome the shortcomings of this approach,an improved Laguerre orthogonal polynomial approach is used in this paper.The correctness and feasibility of this approach are verified by comparing with the results of existing literatures.In the finite thickness coating,the displacement,electric potential and magnetic potential are expanded into Legendre polynomial series,while in the relatively infinite half-space,the displacement,electric potential and magnetic potential are expanded into Laguerre polynomial series.Compared with the conventional Laguerre polynomial approach,the improved approach can obtain the continuous distribution of positive stress,positive electric displacement and positive magnetic induction intensity.Based on the improved laguerre orthogonal polynomial approach,the propagation characteristics of surface waves in multilayer half-space and half-space covered by a functionally graded layer are studied.Results show that the improved Laguerre polynomial approach can solve wave problems of layered half-space correctly;In the multilayer half-space structure with increasing wave velocity,the phase velocity of surface wave decreases with increasing wave number k value.In multilayer half-space structures,the field physical quantities of high-frequency waves are mainly distributed in the low-velocity layer;For half-space structures with gradient cladding,the phase velocity of surface waves decreases with the increase of k value,and as the gradient exponent n increases,the phase velocity decreases and the dispersion becomes more significant;For half-space structures with gradient cladding,the field physical quantities of high frequency waves are mainly distributed near the materials with low wave velocity of the cladding.