Abstract
In this work, analytical solutions to the single scattering of horizontally polarized shear waves (SH) by cylindrical fibers with two specific radially gradient interphase layers are presented. In the first case, the shear modulus μr=e2βr and the square of wave number k2 is a linear function of 1/r; in the second case μr=e−βr2 and k2 is a linear function of r2. As an example, we solve the single scattering of SH waves by a SiC fiber with the two interphase layers in an aluminum matrix. The calculated scattering cross sections are compared to values obtained by an approximate method (dividing the continuous varying layer into multiple homogeneous sublayers). The results indicate the current approach gives excellent performance.
Highlights
Until now the effect of the functional gradient interphase layer on the attenuation of elastic waves in composite materials has been meagerly covered in the literatures [15,16,17,18,19]
Analytical solutions to the single scattering with a radially gradient interphase layer of several specific profiles were provided for shear waves (SH) waves. e derivation process followed the work of Martin [21], in which general solutions to the single scattering of acoustic waves by an inhomogeneous sphere with spherically symmetrical properties were investigated. e two transformations used in our derivation process differed from Martin’s in that the governing equations for distinct waves are different
In this case the shear modulus is an exponential function of r and k2(r) is a linear function of r−1 as given by μ(r) μ1e2βr, k2(r) k21 + 2rα
Summary
As shown, the single scattering of SH waves by a fiber with a radially gradient interphase layer was considered [17]. C(x) μ(x)/ρ(x) is the wave speed, which is a function of position. Only the radial inhomogeneity has been considered; that is, μ(x) and ρ(x) are functions only of the radial coordinate r, so K can be simpli ed to form: K. where k(r) ω/c(r). We seek the solution to equation (6) in the form of the following equation: u(x) un(r)Yn(θ),. Since un is a function of r and Yn is a function of variable θ, so (∇un) · (∇Yn) 0. We know that in the polar coordinate system rnYn(θ) is a separate solution to the Laplace equation as given by. Which is a second-order di erential equation for un(r)
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