The dispersion curves and wave structures of lamb waves in functionally graded plate: Theoretical and simulation analysis

Abstract

Functionally graded materials (FGM) have received extensive attention in recent years for their excellent structural properties. Ultrasonic guided waves (such as Lamb waves) propagated in FGM plates possess obviously dispersion characteristics. Therefore, it is of great value to extract the relationship between the dispersion curves of ultrasound guided waves and the material properties in FGM plates. In this research, the theoretical process of calculating the propagation characteristics of Lamb waves in FGM plates is deduced by combining the FGM volume fraction curve and Legendre polynomial series expansion method. In this proposed method, it avoids slicing the FGM plate into multiple layers. A Mathematica program for numerical calculations was developed, then the Lamb wave dispersion curves were solved. For comparison, the Lamb wave dispersion curves of sliced layer model of a FGM plate is drawn in Disperse software, the results verify the validity of the numerical calculations. Meanwhile, in PZFlex software, the FGM plates was subjected to finite element simulation, also based on the layered plates model. The acoustic characteristics detection experiment (also known as V(f, z) measurement) was performed in the PZFlex simulation, and the Lamb wave dispersion curves were extracted. The influence of the change of the gradient function on Lamb wave dispersion curves was discussed.