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Surface waves in anisotropic elasticity and piezoelectricity, asymptotic analysis and inverse problems

Research Project

Project/Area Number 19K03559
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12020:Mathematical analysis-related
Research InstitutionGunma University

Principal Investigator

田沼 一実  群馬大学, 大学院理工学府, 教授 (60217156)

Project Period (FY) 2019-04-01 – 2025-03-31
Project Status Granted (Fiscal Year 2023)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2022: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2021: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords非等方弾性体 / 圧電体方程式 / 表面波 / Bleustein-Gulyaev波 / Rayleigh波 / transversely isotropic / shear horizontal / 逆問題 / 圧電体 / 摂動 / 横等方 / polarization / 分散 / perturbation / Barnett-Lothe tensors / Stroh formalism / 摂動公式 / 弾性波動 / 位相速度 / 応用解析
Outline of Research at the Start

固体中を伝播する波は,その固体の性質を反映する.固体が弾性体の場合,弾性波の観測により弾性体の非等方性と非斉次性(不均一性)を決定する問題は,材料科学,地球物理,非破壊検査の分野で重要なテーマとなる.固体の性質に関する情報は一般に,そこでの波動現象に複雑に入り込む.しかしながら伝播速度,励起された変位場等の波動現象の一部を観測することで固体の情報をうまく抽出できないか?を根本的問いとして,本研究では非等方弾性体と圧電体を対象に,波動方程式の数学解析により固体パラメターの波動解への寄与の構造を明確にする順問題と,波動解により裏付けられた観測データから固体パラメターを再構成する逆問題とを考察する.

Outline of Annual Research Achievements

1. 圧電体方程式は,圧電体の力学的運動状態と電気的平衡状態を記述し,弾性的応力と電気変位,力学的歪みと電気ポテンシャルの相互関係により,力学的変位と電気ポテンシャルを未知関数とする,弾性・圧電・誘電の3つのテンソルを係数にもつ連立微分方程式となる.弾性場と電場の相互作用は圧電テンソルによって生じるが,等方物質では圧電テンソルが消えるため,非等方性が圧電性の本質と言え,非等方性に対する本研究のこれまでの数学解析が有効となる.横等方(transversely isotropic)圧電体を伝播する表面波の1つ,Bleustein-Gulyaev(BG)波は,境界変位が伝播方向にも境界法線方向にも垂直な,水平横波(shear horizontal)成分のみからなるという特徴をもつ.そこで,横等方圧電体の各テンソルが完全非等方に摂動した場合に,BG波の境界変位は水平横波状態からどのように摂動するかを考察し,水平横波成分からの一次摂動に影響を与える弾性・圧電・誘電のテンソルの成分を,かなり具体的に絞り込むことができた.以上を国際会議International Congress on Industrial and Applied Mathematics(ICIAM 2023)にて報告した.
2. 直交異方性を有する斉次弾性体の弾性テンソルが完全非等方に摂動した場合に,境界におけるRayleigh波のpolarization ratio(境界振幅の伝播方向成分と境界法線方向成分との比)の摂動公式を,論文集「Mathematical Methods and Models in Composites, 2nd edition (World Scientific)」に発表した.論文では,Stroh formalism による非等方弾性体方程式の数学解析も,基礎から丁寧に解き明かしている.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

1.弾性テンソルが直交異方の状態から完全に非等方に摂動した場合に,Rayleigh波の境界におけるpolarization ratioの摂動公式を,論文集「Mathematical Methods and Models in Composites, 2nd edition (World Scientific)」にてようやく出版することができた.
2. Bleustein-Gulyaev(BG)波によって励起される境界変位に対して,その水平横波成分からの一次摂動に関する研究成果の一部を,国際会議International Congress on Industrial and Applied Mathematics (ICIAM 2023) にて報告することができた.

Strategy for Future Research Activity

Bleustein-Gulyaev(BG)波による境界変位場において,その水平横波成分からの一次摂動に,弾性テンソル,圧電テンソル,誘電テンソルの摂動部分がどのように寄与するかを定式化する(順問題).表面波であるBG波の観測により,未知の圧電体の各テンソル,またはその摂動を決定する逆問題の数学解析へ橋渡しを行う.

Report

(5 results)
  • 2023 Research-status Report
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (27 results)

All 2023 2022 2021 2020 2019 Other

All Int'l Joint Research (11 results) Journal Article (6 results) (of which Int'l Joint Research: 5 results,  Peer Reviewed: 3 results) Presentation (9 results) (of which Int'l Joint Research: 6 results,  Invited: 3 results) Funded Workshop (1 results)

  • [Int'l Joint Research] University of Kentucky(米国)

    • Related Report
      2023 Research-status Report
  • [Int'l Joint Research] Zhejiang University(中国)

    • Related Report
      2023 Research-status Report
  • [Int'l Joint Research] Hokkaido University(日本)

    • Related Report
      2023 Research-status Report
  • [Int'l Joint Research] Zhejiang University(中国)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] University of Kentucky/Auburn University at Montgomery(米国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Zhejiang University(中国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Hokkaido University(日本)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Zhejiang University(中国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] University of Kentucky/Auburn University at Montgomery(米国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Zhejiang University(中国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] University of Kentucky/Auburn University at Montgomery(米国)

    • Related Report
      2019 Research-status Report
  • [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 Composites, Second edition2023

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

      Computational and Experimental Methods in Structures (World Scientific)

      Volume: 13 Pages: 333-383

    • DOI

      10.1142/9781800611887_0008

    • ISBN
      9781800611870, 9781800611887
    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Perturbation of Bleustein-Gulyaev waves in piezoelectric media: Barnett and Lothe integral formalism revisited2023

    • Author(s)
      Kazumi Tanuma、Xiang Xu、Gen Nakamura
    • Journal Title

      Journal of Elasticity

      Volume: 153 Issue: 3 Pages: 423-453

    • DOI

      10.1007/s10659-023-10005-0

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Perturbation of phase velocity of Bleustein-Gulyaev waves in piezoelectric media2022

    • Author(s)
      田沼 一実、中村 玄、Xiang Xu
    • Journal Title

      NCTAM papers, National Congress of Theoretical and Applied Mechanics, Japan

      Volume: 66 Issue: 0 Pages: 159

    • DOI

      10.11345/japannctam.66.0_159

    • Related Report
      2022 Research-status Report
    • Int'l Joint Research
  • [Journal Article] Analysis of inverse problems through partial differential equations and related topics, Preface2021

    • Author(s)
      Kazumi Tanuma
    • Journal Title

      数理解析研究所講究録 (RIMS Kokyuroku)

      Volume: 2174

    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Journal Article] On the perturbation of Bleustein-Gulyaev waves in piezoelectric media2021

    • Author(s)
      Gen Nakamura, Kazumi Tanuma and Xiang Xu
    • Journal Title

      Mathematical Analysis of Continuum Mechanics and Industrial Applications, Proceedings of the International Conference CoMFoS18, Springer

      Volume: 掲載決定

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Perturbations of Rayleigh waves in anisotropic elasticity and Bleustein-Gulyaev waves in piezoelectricity2020

    • Author(s)
      Kazumi Tanuma
    • Journal Title

      マス・フォア.インダストリ研究 No.18, New technologies for non-destructive and non-invasive inspections and their applications

      Volume: 18 Pages: 191-233

    • Related Report
      2019 Research-status Report
  • [Presentation] Perturbation of surface waves in piezoelectric media2023

    • Author(s)
      Kazumi Tanuma, Xiang Xu, Gen Nakamura
    • Organizer
      International Congress on Industrial and Applied Mathematics (ICIAM 2023)
    • Related Report
      2023 Research-status Report
    • Int'l Joint Research
  • [Presentation] 圧電体における亜音速表面波の安定性2023

    • Author(s)
      田沼 一実, Xu Xiang, 中村 玄
    • Organizer
      日本応用数理学会第19回研究部会連合発表会
    • Related Report
      2022 Research-status Report
  • [Presentation] 圧電体におけるBleustein-Gulyaev型表面波速度の摂動2022

    • Author(s)
      田沼 一実, Xu Xiang, 中村 玄
    • Organizer
      第66回理論応用力学講演会
    • Related Report
      2022 Research-status Report
  • [Presentation] Dispersion of the polarization ratio of Rayleigh waves in vertically-inhomogeneous and weakly-anisotropic elastic media2022

    • Author(s)
      Kazumi Tanuma, Chi-Sing Man, Yue Chen
    • Organizer
      RIMS Workshop, Theory and practice in inverse problems(RIMS 共同研究(公開型)逆問題における理論と実用)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] Surface waves in anisotropic elasticity and piezoelectricity2022

    • Author(s)
      Kazumi Tanuma
    • Organizer
      IMI Workshop of the Joint Research Project in Kyusyu University, Practical inverse problems and their prospects
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Polarization ratio of Rayleigh waves in vertically-inhomogeneous and weakly-anisotropic elastic media2021

    • Author(s)
      Kazumi Tanuma, Chi-Sing Man, Yue Chen
    • Organizer
      25th International Congress of Theoretical and Applied Mechanics
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] Perturbations of Rayleigh waves in anisotropic elasticity and Bleustein-Gulyaev waves in piezoelectricity2019

    • Author(s)
      Kazumi Tanuma
    • Organizer
      New technologies for non-destructive and non-invasive inspections and their applications, IMI Workshop, Kyusyu University
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 圧電体における表面波速度の摂動2019

    • Author(s)
      田沼一実,中村玄,Xiang Xu
    • Organizer
      日本応用数理学会2019年度年会
    • Related Report
      2019 Research-status Report
  • [Presentation] Perturbation of Bleustein-Gulyaev surface waves in piezoelectric media and a revisit to the Stroh formalism2019

    • Author(s)
      Kazumi Tanuma
    • Organizer
      Summer School on Applied Inverse Problems and Related Topics, Tambara, Gunma
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Funded Workshop] Analysis of Inverse Problems through Partial Differential Equations and Related Topics, Symposium at Research Institute for Mathematical Sciences (RIMS), Kyoto University2020

    • Related Report
      2019 Research-status Report

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Published: 2019-04-18   Modified: 2024-12-25  

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