Some Theoretical and Experimental Extensions Based on the Properties of the Intrinsic Transfer Matrix.

Nicolae Cretu,Hank Steve Andia Prado,Mihail-Ioan Pop

doi:10.3390/ma15020519

Abstract

The work approaches new theoretical and experimental studies in the elastic characterization of materials, based on the properties of the intrinsic transfer matrix. The term ‘intrinsic transfer matrix’ was firstly introduced by us in order to characterize the system in standing wave case, when the stationary wave is confined inside the sample. An important property of the intrinsic transfer matrix is that at resonance, and in absence of attenuation, the eigenvalues are real. This property underlies a numerical method which permits to find the phase velocity for the longitudinal wave in a sample. This modal approach is a numerical method which takes into account the eigenvalues, which are analytically estimated for simple elastic systems. Such elastic systems are characterized by a simple distribution of eigenmodes, which may be easily highlighted by experiment. The paper generalizes the intrinsic transfer matrix method by including the attenuation and a study of the influence of inhomogeneity. The condition for real eigenvalues in that case shows that the frequencies of eigenmodes are not affected by attenuation. For the influence of inhomogeneity, we consider a case when the sound speed is varying along the layer’s length in the medium of interest, with an accompanying dispersion. The paper also studies the accuracy of the method in estimating the wave velocity and determines an optimal experimental setup in order to reduce the influence of frequency errors.

Highlights

A transfer matrix is an important tool in the study of wave and pulse propagation in finite and infinite homogeneous and inhomogeneous elastic media
The method is widely used in computer simulation or in elastic characterization of different kinds of elastic media [1,2,3]
The downside of matrix methods is that, while they are well adapted to 1D wave propagation, for larger dimensions they require complicated transfer matrices which are harder to work with and interpret in terms of involved wave phenomena

Summary

Introduction

A transfer matrix is an important tool in the study of wave and pulse propagation in finite and infinite homogeneous and inhomogeneous elastic media. The intrinsic transfer matrix was applied to study the behavior of a multilayered medium with inhomogeneities, by considering the case in which one layer consists of a non-homogeneous material. One possible effect of inhomogeneity is the appearance of dispersion, i.e., frequency-dependent sound velocity This is applied in the case of multilayered media, and for polycrystalline materials composed of anisotropic grains such as metals, or for metamaterials in a larger sense. The case of a ternary elastic system is being analyzed, but the study may be generalized to other complex multilayered media

The Idea of an Intrinsic Transfer Matrix

4.. Conclusions