Lamb waves in multilayered media: 3D and 6D formalisms

Anna Avershyeva,Sergey Kuznetsov,A Volkov,A Adamtsevich,T Sultanov,A Pustovgar

doi:10.1051/e3sconf/20199703003

Anna Avershyeva, Sergey Kuznetsov + Show 4 more

Open Access

https://doi.org/10.1051/e3sconf/20199703003

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Abstract

A mathematical model for analyzing Lamb waves propagating in stratified media with arbitrary elastic anisotropy is worked out. The model incorporates a combined Fundamental Matrix (FM) and Modified Transfer Matrix (MTM) methods. Multilayered unbounded plates with different types of boundary conditions imposed on the outer surfaces are considered. Closed form fundamental matrices and secular equations for dispersion relations are derived.

Highlights

The genuine Lamb waves [1] are surface acoustic waves propagating in an unbounded isotropic homogeneous plate subjected to traction-free boundary conditions at the outer planes: isotropic homogeneous plate subjected to traction-free boundary conditions at the outer planes: t (x,t)
In (1.1) t are surface tractions, is the unit normal to one of the boundary planes, C is the fourth order elasticity tensor, u is the displacement field, t is time, x x is the coordinate normal to the plane x 0, and h is the depth of a plate; see, Fig.1, where n is the unit vector normal to the wave front
In the present paper a different six-dimensional formalism developed in [17, 18] will be used. Applying this formalism will allow us to obtain closed form fundamental matrices and secular equations for Lamb waves propagating in multilayered plates with arbitrary elastic anisotropy

Summary

Introduction

The genuine Lamb waves [1] are surface acoustic waves propagating in an unbounded isotropic homogeneous plate subjected to traction-free boundary conditions at the outer planes: isotropic homogeneous plate subjected to traction-free boundary conditions at the outer planes:. Where Ck are the unknown complex coefficients defined up to a multiplier from the boundary or interface conditions (1.1) – (1.5); mk are the unknown polarization vectors; fk are unknown scalar complex-valued functions; the exponential multiplier eir(n ct) corresponds to propagation of the plane wave front along direction n with the phase speed c ; r is the wave number; dimensionless coordinate x in (1.7) is defined by x irx. An alternative approach will be introduced, which removes necessity to create and analyze vectors mk and functions fk Applying this formalism will allow us to obtain closed form fundamental matrices and secular equations for Lamb waves propagating in multilayered plates with arbitrary elastic anisotropy

Governing equations Equation Section 2

Traction-free plate

Clamped plate

Conclusions