Forced guided waves in linearly elastic plates (II) – A modified normal-mode expansion method

Abstract

The classical normal-mode expansion method developed by Auld and Kino in 1973 has been used widely by numerous researchers and practitioners to study forced guided waves in plates and layered media, including both elastic and electromagnetic waves. However, it was shown in Part I of this study that, although this method gives the correct solution when applied to horizontally polarized shear waves and electromagnetic waves, it does not yield the correct elastodynamic solution when applied to Lamb waves. To address this shortcoming, we develop in this paper a modified normal-mode expansion method that yields the correct elastodynamic solution in that the solution satisfies all the elastodynamic governing equations and the boundary conditions for forced Lamb waves in a plate. The efficacy of the modified normal-mode expansion method is further confirmed by comparing its solution with the finite element solution. Further, it is showed that when applied to horizontally polarized shear waves, the modified normal-mode expansion method yields numerically the same result as that of the classical normal-mode expansion method. However, the modified normal-mode expansion solution converges much faster.