The Method Of Finite Spheres For Ultrasonic Scattering Of Defects In Thin Plates

Ultrasonic Lamb Wave detection technology is widely used in all major areas of thin plate health testing,it is a more advanced nondestructive testing technology.Because of the dispersion characteristics of lamb wave,its application in the actual industrial production has certain limitations.In order to determine the propagation state of lamb wave,we have a clearer understanding of the process of lamb wave propagating in the plate,this paper studies the dispersion characteristic of lamb wave,the propagation state,and applies the finite sphere method to the numerical simulation of lamb wave,and compares it with the experimental result.As a meshless method,finite sphere method not only avoids the defect of dispersion error of the finite element method in solving wave propagation problem,but also has some advantages in solving the structure of domain discretization and interpolation function.In this paper,the basic theory of finite sphere method is expounded,including the discretization of its solution domain,the selection of shape function,the structure of interpolation function,the application of boundary condition,the selection of numerical integration scheme and the derivation of basic equation.The dispersion characteristic of lamb wave is the most important characteristic,and the frequency dispersion equation of lamb wave is obtained by using the potential function method through its wave equation.By using the idea of classified discussion,the relationship between the group velocity and the phase velocity and the frequency thick product of lamb wave is obtained,and the dispersion curve of lamb wave is plotted by MATLAB programming.The finite sphere method is applied to the numerical simulation of lamb wave.The wave equation of lamb wave is solved by finite sphere method,the mass matrix and stiffness matrix are obtained,the bathe integral scheme is selected on the time integration scheme,and the finite sphere method is used to numerical modeling the propagation state of the lamb wave in the thin plate,and the reliability and accuracy of the finite sphere method are verified by comparing with the experimental results.