Iterative solution to bulk wave propagation in polycrystalline materials

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This article reevaluates two foundational models for bulk ultrasonic wave propagation in polycrystals. A decoupling of real and imaginary parts of the effective wave number permits a simple iterative method to obtain longitudinal and shear wave attenuation constants and phase velocity relations. The zeroth-order solution is that of Weaver [J. Mech. Phys. Solids 38, 55-86 (1990)]. Continued iteration converges to the unified theory solution of Stanke and Kino [J. Acoust. Soc. Am. 75, 665-681 (1984)]. The converged solution is valid for all frequencies. The iterative method mitigates the need to solve a nonlinear, complex-valued system of equations, which makes the models more robust and accessible to researchers. An analysis of the variation between the solutions is conducted and is shown to be proportional to the degree of inhomogeneity in the polycrystal.

Original languageEnglish (US)
Pages (from-to)1804-1811
Number of pages8
JournalJournal of the Acoustical Society of America
Volume141
Issue number3
DOIs
StatePublished - Mar 1 2017

Fingerprint

iterative solution
wave propagation
polycrystals
wave attenuation
longitudinal waves
ultrasonic radiation
complex systems
phase velocity
decoupling
S waves
iteration
inhomogeneity
Waves
Bulk

All Science Journal Classification (ASJC) codes

  • Arts and Humanities (miscellaneous)
  • Acoustics and Ultrasonics

Cite this

@article{37b467b2a6174dc5a7b8995f1ad198d7,
title = "Iterative solution to bulk wave propagation in polycrystalline materials",
abstract = "This article reevaluates two foundational models for bulk ultrasonic wave propagation in polycrystals. A decoupling of real and imaginary parts of the effective wave number permits a simple iterative method to obtain longitudinal and shear wave attenuation constants and phase velocity relations. The zeroth-order solution is that of Weaver [J. Mech. Phys. Solids 38, 55-86 (1990)]. Continued iteration converges to the unified theory solution of Stanke and Kino [J. Acoust. Soc. Am. 75, 665-681 (1984)]. The converged solution is valid for all frequencies. The iterative method mitigates the need to solve a nonlinear, complex-valued system of equations, which makes the models more robust and accessible to researchers. An analysis of the variation between the solutions is conducted and is shown to be proportional to the degree of inhomogeneity in the polycrystal.",
author = "Christopher Kube",
year = "2017",
month = "3",
day = "1",
doi = "10.1121/1.4978008",
language = "English (US)",
volume = "141",
pages = "1804--1811",
journal = "Journal of the Acoustical Society of America",
issn = "0001-4966",
publisher = "Acoustical Society of America",
number = "3",

}

Iterative solution to bulk wave propagation in polycrystalline materials. / Kube, Christopher.

In: Journal of the Acoustical Society of America, Vol. 141, No. 3, 01.03.2017, p. 1804-1811.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Iterative solution to bulk wave propagation in polycrystalline materials

AU - Kube, Christopher

PY - 2017/3/1

Y1 - 2017/3/1

N2 - This article reevaluates two foundational models for bulk ultrasonic wave propagation in polycrystals. A decoupling of real and imaginary parts of the effective wave number permits a simple iterative method to obtain longitudinal and shear wave attenuation constants and phase velocity relations. The zeroth-order solution is that of Weaver [J. Mech. Phys. Solids 38, 55-86 (1990)]. Continued iteration converges to the unified theory solution of Stanke and Kino [J. Acoust. Soc. Am. 75, 665-681 (1984)]. The converged solution is valid for all frequencies. The iterative method mitigates the need to solve a nonlinear, complex-valued system of equations, which makes the models more robust and accessible to researchers. An analysis of the variation between the solutions is conducted and is shown to be proportional to the degree of inhomogeneity in the polycrystal.

AB - This article reevaluates two foundational models for bulk ultrasonic wave propagation in polycrystals. A decoupling of real and imaginary parts of the effective wave number permits a simple iterative method to obtain longitudinal and shear wave attenuation constants and phase velocity relations. The zeroth-order solution is that of Weaver [J. Mech. Phys. Solids 38, 55-86 (1990)]. Continued iteration converges to the unified theory solution of Stanke and Kino [J. Acoust. Soc. Am. 75, 665-681 (1984)]. The converged solution is valid for all frequencies. The iterative method mitigates the need to solve a nonlinear, complex-valued system of equations, which makes the models more robust and accessible to researchers. An analysis of the variation between the solutions is conducted and is shown to be proportional to the degree of inhomogeneity in the polycrystal.

UR - http://www.scopus.com/inward/record.url?scp=85015386727&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015386727&partnerID=8YFLogxK

U2 - 10.1121/1.4978008

DO - 10.1121/1.4978008

M3 - Article

VL - 141

SP - 1804

EP - 1811

JO - Journal of the Acoustical Society of America

JF - Journal of the Acoustical Society of America

SN - 0001-4966

IS - 3

ER -