---
_id: '14008'
abstract:
- lang: eng
text: Computer aided simulation of guided acoustic waves in single- or multilayered
waveguides is an essential tool for several applications of acoustics and ultrasonics
(i.e. pipe inspection, noise reduction). To simulate wave propagation in geometrically
simple waveguides (plates or rods), one may employ the analytical global matrix
method [1]. This requires the computation of all roots of the determinate of a
certain submatrix. The evaluation of all real or even complex roots is actually
the methods most concerning restriction. Previous approaches base on so called
mode-tracers which use the physical phenomenon that solutions (roots) appear in
a certain pattern (waveguide modes) and thus use known solutions to limit the
root finding algorithms searchspace with respect to consecutive solutions. As
the limitation of searchspace might be unstable in some cases, we propose to replace
the mode-tracer with a suitable version of an interval Newton method based on
Intlab [2]. To apply this interval based method, we extended the interval and
derivative computation provided by Intlab such that corresponding information
is also available for Bessel functions used in the circular model (rods) of acoustic
waveguides. We present numerical results of a simple acoustic waveguide and discuss
extensions required for more realistic scenarios.
author:
- first_name: Andrea
full_name: Walther, Andrea
last_name: Walther
- first_name: Fabian
full_name: Bause, Fabian
last_name: Bause
- first_name: Bernd
full_name: Henning, Bernd
id: '213'
last_name: Henning
citation:
ama: 'Walther A, Bause F, Henning B. Computing roots for the analytic modeling of
guided waves in acoustic waveguides. In: ; 2012.'
apa: Walther, A., Bause, F., & Henning, B. (2012). Computing roots for the analytic
modeling of guided waves in acoustic waveguides. Presented at the 83rd Annual
Meeting of the International Association of Applied Mathematics and Mechanics
(GAMM), Darmstadt.
bibtex: '@inproceedings{Walther_Bause_Henning_2012, title={Computing roots for the
analytic modeling of guided waves in acoustic waveguides}, author={Walther, Andrea
and Bause, Fabian and Henning, Bernd}, year={2012} }'
chicago: Walther, Andrea, Fabian Bause, and Bernd Henning. “Computing Roots for
the Analytic Modeling of Guided Waves in Acoustic Waveguides,” 2012.
ieee: A. Walther, F. Bause, and B. Henning, “Computing roots for the analytic modeling
of guided waves in acoustic waveguides,” presented at the 83rd Annual Meeting
of the International Association of Applied Mathematics and Mechanics (GAMM),
Darmstadt, 2012.
mla: Walther, Andrea, et al. *Computing Roots for the Analytic Modeling of Guided
Waves in Acoustic Waveguides*. 2012.
short: 'A. Walther, F. Bause, B. Henning, in: 2012.'
conference:
end_date: 30.03.2012
location: Darmstadt
name: 83rd Annual Meeting of the International Association of Applied Mathematics
and Mechanics (GAMM)
start_date: 26.03.2012
date_created: 2019-10-24T14:11:31Z
date_updated: 2022-01-06T06:51:49Z
department:
- _id: '49'
language:
- iso: eng
status: public
title: Computing roots for the analytic modeling of guided waves in acoustic waveguides
type: conference
user_id: '15911'
year: '2012'
...