Modeling Of The Propagation Characteristics Of Lamb Waves Using Spectral Finite Element Method

Structural health monitoring technology is a key issue in the study of smart material and structures. With the development of computer technique, due to the intelligence, damage detection based on Lamb waves is widely used and deeply studied in the field of structural health monitoring technology. At present, the shortcoming in the traditional methods of modeling Lamb waves is that it is difficult to get the results accurately and efficiently in the structures with small fatigue damage.This paper takes an isotropic rod and an isotropic plate structure as the main objects of this study. For detection of small fatigue damage in structures, a popular method in non-destructive testing based on Lamb waves is used in this study, and the propagation characteristics of Lamb waves and Lamb waves in the plate are also analysed. Then,a new tool for numerical modeling of elastic wave propagation——the theory of the SEM based on the Legendre polynominals is introduced, which is more accurate and efficient than the classical FEM method. In structural health monitoring, the solving process of classical FEM method to a small fatigue damage is time consuming and the result is not perfect. On the contrary,this is the advantage of spectral finite element, which leads to the diagonal form of the mass matrix, allows a crucial reduction of the algorithm, and improves the accuracy of the solution. In this paper, the ultrasonic detection technique of Lamb waves in the area of non-destructive testing is used. Based on the numerical modeling of elastic wave propagation using Legendre SEM, the derivation of basic theoretical equations of SEM is obtained.During the process of computing, the idea of componentwise is used to decrease the time-consuming,and the technology in this paper has better performance is proved through the examples of an isotropic rod and an isotropic plate.