Cauchy Six-Dimensional Formalism for Lamb Waves in Multilayered Plates

Sergey V Kuznetsov

doi:10.1155/2013/698706

Abstract

Propagation of Lamb waves in multilayered elastic anisotropic plates is studied in the framework of combination of the six-dimensional Cauchy formalism and the transfer matrix method. The closed form secular equations for dispersion curves of Lamb waves propagating in multilayered plates with arbitrary elastic anisotropy are obtained.

Highlights

A brief introduction to the theory of Lamb waves and a review of some of the most important works on this matter are presented.1.1
In the first works on Lamb waves propagating in anisotropic plates, a three-dimensional formalism was used
In [56, 57], the Stroh formalism was applied to the description of Lamb waves propagating in the homogeneous anisotropic plates

Summary

Introduction

A brief introduction to the theory of Lamb waves and a review of some of the most important works on this matter are presented. Analysis of (16) at rh → 0 (the long wave limit) yields the following equation [5]: γ2 γ1. Numerical studies [19,20,21,22,23,24,25] of the group velocity dispersion, mainly at Poisson’s condition λ = μ, confirmed Rayleigh’s anticipation [16, 17] that the negative values of the group velocity can appear at the very small wave numbers. Substituting the phase speed defined by (11) into (13), denoting the left-hand side of (16) by F±(r, ω), and assuming that ω is a function of r, the derivative of (16) with respect to r takes the form. Theoretical studies of the phase, group, and ray velocities were done in [26]

Homogeneous Anisotropic Plates

Multilayered Plates

Cauchy Six-Dimensional Formalism

Numerical Examples

Conclusion