Lamb waves in functionally graded plates: Proof of stratification convergence

Abstract

Lamb waves propagating in anisotropic functionally graded (FG) plates with an arbitrary continuous transverse inhomogeneity are considered. Along with the FG plates, stratified ones with the homogeneous physical properties inside the individual layers, are considered. Theorem on convergence of dispersion curves in stratified plates to the corresponding dispersion curves in the FG plates is proved, allowing one to analyze dispersion of Lamb waves in FG plates by constructing the less complicated solutions related to stratified plates. Numerical examples for isotropic FG and stratified plates are considered.

Keywords:

• Lamb wave
• secular equation
• velocity
• convergence
• Cauchy formalism

Acknowledgements

The work was supported by the Russian Science Foundation (Grant 20-49-08002).