IEICE TRANSACTIONS on Fundamentals
Application of the Recursive Transfer Method to Flexural Waves I: Novel Discretization Scheme Using Weak Form Theory Framework and Waveguide Modes on Inhomogeneous Elastic Plates
Summary :
Flexural waves on a thin elastic plate are governed by the fourth-order differential equation, which is attractive not only from a harmonic analysis viewpoint but also useful for an efficient numerical method in the elastdynamics. In this paper, we proposed two novel ideas: (1) use of the tensor bases to describe flexural waves on inhomogeneous elastic plates, (2) weak form discretization to derive the second-order difference equation from the fourth-order differential equation. The discretization method proposed in this study is of preliminary consideration about the recursive transfer method (RTM) to analyse the scattering problem of flexural waves. More importantly, the proposed discretization method can be applied to any system which can be formulated by the weak form theory. The accuracy of the difference equation derived by the proposed discretization method is confirmed by comparing the analytical and numerical solutions of waveguide modes. As a typical problem to confirm the validity of the resultant governing equation, the influence of the spatially modulated elastic constant in waveguide modes is discussed.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E97-A No.5 pp.1075-1085
- Publication Date
- 2014/05/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E97.A.1075
- Type of Manuscript
- PAPER
- Category
- Numerical Analysis and Optimization
Authors
Hatsuhiro KATO
University of Yamanashi
Hatsuyoshi KATO
Tomakomai National College of Technology
Keyword
Latest Issue
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Hatsuhiro KATO, Hatsuyoshi KATO, "Application of the Recursive Transfer Method to Flexural Waves I: Novel Discretization Scheme Using Weak Form Theory Framework and Waveguide Modes on Inhomogeneous Elastic Plates" in IEICE TRANSACTIONS on Fundamentals,
vol. E97-A, no. 5, pp. 1075-1085, May 2014, doi: 10.1587/transfun.E97.A.1075.
Abstract: Flexural waves on a thin elastic plate are governed by the fourth-order differential equation, which is attractive not only from a harmonic analysis viewpoint but also useful for an efficient numerical method in the elastdynamics. In this paper, we proposed two novel ideas: (1) use of the tensor bases to describe flexural waves on inhomogeneous elastic plates, (2) weak form discretization to derive the second-order difference equation from the fourth-order differential equation. The discretization method proposed in this study is of preliminary consideration about the recursive transfer method (RTM) to analyse the scattering problem of flexural waves. More importantly, the proposed discretization method can be applied to any system which can be formulated by the weak form theory. The accuracy of the difference equation derived by the proposed discretization method is confirmed by comparing the analytical and numerical solutions of waveguide modes. As a typical problem to confirm the validity of the resultant governing equation, the influence of the spatially modulated elastic constant in waveguide modes is discussed.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E97.A.1075/_p
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@ARTICLE{e97-a_5_1075,
author={Hatsuhiro KATO, Hatsuyoshi KATO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Application of the Recursive Transfer Method to Flexural Waves I: Novel Discretization Scheme Using Weak Form Theory Framework and Waveguide Modes on Inhomogeneous Elastic Plates},
year={2014},
volume={E97-A},
number={5},
pages={1075-1085},
abstract={Flexural waves on a thin elastic plate are governed by the fourth-order differential equation, which is attractive not only from a harmonic analysis viewpoint but also useful for an efficient numerical method in the elastdynamics. In this paper, we proposed two novel ideas: (1) use of the tensor bases to describe flexural waves on inhomogeneous elastic plates, (2) weak form discretization to derive the second-order difference equation from the fourth-order differential equation. The discretization method proposed in this study is of preliminary consideration about the recursive transfer method (RTM) to analyse the scattering problem of flexural waves. More importantly, the proposed discretization method can be applied to any system which can be formulated by the weak form theory. The accuracy of the difference equation derived by the proposed discretization method is confirmed by comparing the analytical and numerical solutions of waveguide modes. As a typical problem to confirm the validity of the resultant governing equation, the influence of the spatially modulated elastic constant in waveguide modes is discussed.},
keywords={},
doi={10.1587/transfun.E97.A.1075},
ISSN={1745-1337},
month={May},}
Copy
TY - JOUR
TI - Application of the Recursive Transfer Method to Flexural Waves I: Novel Discretization Scheme Using Weak Form Theory Framework and Waveguide Modes on Inhomogeneous Elastic Plates
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1075
EP - 1085
AU - Hatsuhiro KATO
AU - Hatsuyoshi KATO
PY - 2014
DO - 10.1587/transfun.E97.A.1075
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E97-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2014
AB - Flexural waves on a thin elastic plate are governed by the fourth-order differential equation, which is attractive not only from a harmonic analysis viewpoint but also useful for an efficient numerical method in the elastdynamics. In this paper, we proposed two novel ideas: (1) use of the tensor bases to describe flexural waves on inhomogeneous elastic plates, (2) weak form discretization to derive the second-order difference equation from the fourth-order differential equation. The discretization method proposed in this study is of preliminary consideration about the recursive transfer method (RTM) to analyse the scattering problem of flexural waves. More importantly, the proposed discretization method can be applied to any system which can be formulated by the weak form theory. The accuracy of the difference equation derived by the proposed discretization method is confirmed by comparing the analytical and numerical solutions of waveguide modes. As a typical problem to confirm the validity of the resultant governing equation, the influence of the spatially modulated elastic constant in waveguide modes is discussed.
ER -
English
