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Asymptotic analysis for wave propagation in elasticity and inverse problems

Research Project

Project/Area Number 22540111
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionGunma University

Principal Investigator

TANUMA Kazumi  群馬大学, 理工学研究院, 准教授 (60217156)

Co-Investigator(Renkei-kenkyūsha) NAKAMURA Gen  韓国・仁荷大学, 北海道大学, 数学科, 理学研究科, 教授 (50118535)
Research Collaborator CHI-SING Man  アメリカ合衆国・ケンタッキー大学, 数学科, 教授
Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords応用解析 / 弾性波 / 非等方弾性体 / Rayleigh 波 / 残留応力 / 逆問題 / Stroh formalism / surface impedance / 国際研究者交流 / アメリカ合衆国 / 弾性波動方程式 / 分散と摂動 / 弾性界面波 / 弾性表面波 / Stoneley 波 / 分散 / Rayleigh波 / 直交異方性 / fiber-reinforced composites / 摂動公式 / 分散公式 / 弾性波動 / 位相速度
Research Abstract

In this research project we obtain a high-frequency asymptotic formula for the velocity of elastic surface waves (Rayleigh waves) which propagate along the surface of an inhomogeneous, anisotropic elastic media. This formula expresses the frequency-dependence of the Rayleigh-wave velocity, i.e., the dispersion of Rayleigh waves, as caused by the inhomogeneity of the medium. We also give a formula for the first-order perturbation of the velocity of Rayleigh waves and give a formula for that of interfacial waves which propagate along the bonded interface between two dissimilar semi-infinite anisotropic elastic media, as caused by the anisotropy of the media. These results can be applied to the inverse problems in non-destructive evaluation, seismology, and materials science, i.e., the problem of determining the anisotropy and the inhomogeneity of elastic media with initial stresses from boundary measurement of velocities of the aforementioned elastic waves.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (32 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (8 results) (of which Peer Reviewed: 7 results) Presentation (24 results) (of which Invited: 2 results)

  • [Journal Article] Dispersion of Rayleigh Waves in Vertically-Inhomogeneous Prestressed Elastic Media2013

    • Author(s)
      Chi-Sing Man,Gen Nakamura,Kazumi Tanuma and Shengzhang Wang
    • Journal Title

      IMA Journal of Applied Mathematics

      Volume: (in press) Issue: 1 Pages: 1-38

    • DOI

      10.1093/imamat/hxt025

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Propagation of Rayleigh waves in anisotropic media and an inverse problem in the characterization of initial stress : in Mathematical Methods and Models in Composites2013

    • Author(s)
      Kazumi Tanuma and Chi-Sing Man
    • Journal Title

      World Scientific(V. Mantic (ed.), Imperial College Press)

      Volume: (ISBN:978-1-84816-784-1) Pages: 209-246

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Perturbation of phase velocity of Rayleigh waves in pre-stressed anisotropic media with orthorhombic principal part2013

    • Author(s)
      Kazumi Tanuma, Chi-Sing Man and Wenwen Du
    • Journal Title

      Mathematics and Mechanics of Solids

      Volume: 18 Pages: 301-322

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Perturbation of Rayleigh waves and interfacial waves in anisotropic elastic media2013

    • Author(s)
      Kazumi Tanuma
    • Journal Title

      Workshop on Boundary Phenomena for Evolutionary Partial Differential Equations, Abstract and Program

      Volume: - Pages: 8-8

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Propagation of Rayleigh waves in an isotropic media and an inverse problem in characterization of initial stress2012

    • Author(s)
      Kazumi Tanuma
    • Journal Title

      Mathematical Methods and Models in Composites (V.Mantic ed.), Imperial College Press, London

      Volume: (印刷中)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Recovering conductivity at the boundary in three-dimensional electrical impedance tomography2011

    • Author(s)
      Gen Nakamura, Paivi Ronkanen, Samuli Siltanen and Kazumi Tanuma
    • Journal Title

      Inverse Problems and Imaging

      Volume: 5 Pages: 485-510

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Recovering conductivity at the boundary in three-dimensional electrical impedance tomography2011

    • Author(s)
      Gen Nakamura
    • Journal Title

      Inverse Problems and Imaging

      Volume: Vol.5 Issue: 2 Pages: 485-510

    • DOI

      10.3934/ipi.2011.5.485

    • Related Report
      2011 Annual Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Perturbation of phase velocity of Rayleigh waves in pre-stressed anisotropic media with orthorhombic principal part

    • Author(s)
      Kazumi Tanuma
    • Journal Title

      Mathematics and Mechanics of Solids

      Volume: (印刷中)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Perturbation and Dispersion of Rayleigh Waves in Prestressed Anisotropic Elastic Media2014

    • Author(s)
      Kazumi Tanuma
    • Organizer
      Inverse Problems Seminar, Finnish Inverse Problems Society
    • Place of Presentation
      University of Helsinki, Helsinki, Finland
    • Year and Date
      2014-03-24
    • Related Report
      2013 Final Research Report
  • [Presentation] Perturbation of Rayleigh waves and interfacial waves in anisotropic elastic media2013

    • Author(s)
      Kazumi Tanuma, Chi-Sing Man and Wenwen Du
    • Organizer
      Workshop on Boundary Phenomena for Evolutionary Partial Differential Equations
    • Place of Presentation
      Institute of Mathematics, Academia Sinica, Taipei, Taiwan
    • Year and Date
      2013-04-19
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 非等方弾性体におけるStoneley波速度の摂動2013

    • Author(s)
      田沼一実
    • Organizer
      第62回理論応用力学講演会,オーガナイズドセッション:波動現象の数理とその応用
    • Place of Presentation
      東京工業大学,東京
    • Year and Date
      2013-03-07
    • Related Report
      2013 Final Research Report
  • [Presentation] 非等方弾性体におけるRayleigh wavesおよびinterfacial wavesの位相速度の摂動2013

    • Author(s)
      田沼一実
    • Organizer
      現象解析特別セミナー第3回
    • Place of Presentation
      群馬大学工学部,桐生
    • Year and Date
      2013-03-02
    • Related Report
      2013 Final Research Report
  • [Presentation] Dispersion of Rayleigh waves in vertically-inhomogeneous prestressed elastic media2012

    • Author(s)
      Kazumi Tanuma
    • Organizer
      Seminar in mathematics of materials
    • Place of Presentation
      University of Kentucky, Lexingtonアメリカ合衆国
    • Year and Date
      2012-09-28
    • Related Report
      2013 Final Research Report
  • [Presentation] 直交異方性弾性体からのRayleigh波およびStoneley波の位相速度の摂動2012

    • Author(s)
      田沼一実
    • Organizer
      日本数学会秋季総合分科会・応用数学分科会
    • Place of Presentation
      九州大学大学院数理学研究院,福岡
    • Year and Date
      2012-09-21
    • Related Report
      2013 Final Research Report
  • [Presentation] 直交異方性弾性体からのRayleigh波速度の摂動2012

    • Author(s)
      田沼一実
    • Organizer
      数理科学セミナー
    • Place of Presentation
      同志社大学,京都
    • Year and Date
      2012-03-11
    • Related Report
      2013 Final Research Report
  • [Presentation] 直交異方性弾性体からのRayleigh波速度の摂動2012

    • Author(s)
      田沼一実
    • Organizer
      数理科学セミナー
    • Place of Presentation
      同志社大学 京都市
    • Year and Date
      2012-03-11
    • Related Report
      2011 Annual Research Report
  • [Presentation] 直交異方性弾性体からのRayleigh波速度の摂動2012

    • Author(s)
      田沼一実, Chi-Sing Man and Wenwen Du
    • Organizer
      第61回理論応用力学講演会,オーガナイズドセッション:波動現象の数理とその応用
    • Place of Presentation
      東京大学生産技術研究所,東京
    • Year and Date
      2012-03-09
    • Related Report
      2013 Final Research Report
  • [Presentation] 直交異方性弾性体からのRayleigh波速度の摂動2012

    • Author(s)
      田沼一実
    • Organizer
      第61回理論応用力学講演会,オーガナイズドセッション:波動現象の数理とその応用
    • Place of Presentation
      東京大学生産技術研究所 東京都
    • Year and Date
      2012-03-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Perturbation of phase velocity of Rayleigh waves in anisotropic elastic media with orthorhombic principal part2011

    • Author(s)
      Kazumi Tanuma, Chi-Sing Man and Wenwen Du
    • Organizer
      Finnish-Japanese-Korean Workshop on Inverse Problems
    • Place of Presentation
      University of Helsinki, Helsinki, Finland
    • Year and Date
      2011-12-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Perturbation of phase velocity of Rayleigh waves in anisotropic elastic media with orthorhombic principal part2011

    • Author(s)
      Kazumi Tanuma
    • Organizer
      Finnish-Japanese-Korean Workshop on Inverse Problems
    • Place of Presentation
      University of Helsinki Helsinki, Finland
    • Year and Date
      2011-12-13
    • Related Report
      2011 Annual Research Report
  • [Presentation] Perturbation and dispersion of phase velocity of Rayleigh waves in prestressed anisotropic elastic media2010

    • Author(s)
      Kazumi Tanuma
    • Organizer
      数理科学セミナー
    • Place of Presentation
      大阪電気通信大学,大阪府寝屋川市
    • Year and Date
      2010-09-20
    • Related Report
      2013 Final Research Report
  • [Presentation] Perturbation and dispersion of phase velocity of Rayleigh waves in prestressed anisotropic elastic media2010

    • Author(s)
      Kazumi Tanuma
    • Organizer
      数理科学セミナー
    • Place of Presentation
      大阪電気通信大学(大阪市寝屋川市)
    • Year and Date
      2010-09-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] Dispersion of phase velocity of Rayleigh waves in prestressed anisotropic elastic media2010

    • Author(s)
      田沼一実, Chi-Sing Man, Gen Nakamura, and Shengzhang Wang
    • Organizer
      京都大学数理解析研究所研究集会「偏微分方程式の逆問題解析とその周辺分野に関する研究」
    • Place of Presentation
      京都大学,京都
    • Year and Date
      2010-06-23
    • Related Report
      2013 Final Research Report
  • [Presentation] Dispersion of phase velocity of Rayleigh waves in prestressed anisotropic elastic media2010

    • Author(s)
      田沼一実
    • Organizer
      京都大学数理解析研究所研究集会「偏微分方程式の逆問題解析とその周辺分野に関する研究」
    • Place of Presentation
      京都大学(京都市)
    • Year and Date
      2010-06-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Perturbation and dispersion of Rayleigh waves in prestressed anisotropic elastic media2010

    • Author(s)
      Kazumi Tanuma, Chi-Sing Man, Gen Nakamura, and Shengzhang Wang
    • Organizer
      The Third International Conference on Dynamics, Vibration and Control
    • Place of Presentation
      杭州大学,杭州市,中国
    • Year and Date
      2010-05-13
    • Related Report
      2013 Final Research Report
  • [Presentation] Perturbation and dispersion of Rayleigh waves in prestressed anisotropic elastic media2010

    • Author(s)
      Kazumi Tanuma
    • Organizer
      The Third International Conference on Dynamics, Vibration and Control?
    • Place of Presentation
      杭州大学(中国,杭州市)
    • Year and Date
      2010-05-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] Perturbation of Rayleigh waves and interfacial waves in anisotropic elastic media

    • Author(s)
      Kazumi Tanuma, Chi-Sing Man and Wenwen Du
    • Organizer
      Workshop on Boundary Phenomena for Evolutionary Partial Differential Equations
    • Place of Presentation
      Institute of Mathematics, Academia Sinica, Taipei, Taiwan
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Perturbation and Dispersion of Rayleigh Waves in Prestressed Anisotropic Elastic Media

    • Author(s)
      Kazumi Tanuma
    • Organizer
      Inverse Problems Seminar
    • Place of Presentation
      Finnish Inverse Problems Society, University of Helsinki, Helsinki, Finland
    • Related Report
      2013 Annual Research Report
  • [Presentation] 非等方弾性体におけるStoneley波速度の摂動

    • Author(s)
      田沼一実
    • Organizer
      第62回理論応用力学講演会,オーガナイズドセッション:波動現象の数理とその応用
    • Place of Presentation
      東京工業大学( 東京都)
    • Related Report
      2012 Annual Research Report
  • [Presentation] 非等方弾性体におけるRayleigh waves およびinterfacial waves の位相速度の摂動

    • Author(s)
      田沼一実
    • Organizer
      現象解析特別セミナー第3回
    • Place of Presentation
      群馬大学工学部( 桐生市)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Dispersion of Rayleigh waves in vertically-inhomogeneous prestressed elastic media

    • Author(s)
      Kazumi Tanuma
    • Organizer
      Seminar in mathematics of materials
    • Place of Presentation
      University of Kentucky (Lexington アメリカ合衆国)
    • Related Report
      2012 Annual Research Report
  • [Presentation] 直交異方性弾性体からのRayleigh波およびStoneley波の位相速度の摂動

    • Author(s)
      田沼一実
    • Organizer
      日本数学会秋季総合分科会・応用数学分科会
    • Place of Presentation
      九州大学大学院数理学研究院( 福岡市)
    • Related Report
      2012 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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