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Group theoretical analysis for nonlinear normal mode of solids

Research Project

Project/Area Number 16K14117
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Materials/Mechanics of materials
Research InstitutionOsaka University

Principal Investigator

Tarumi Ryuichi  大阪大学, 工学研究科, 准教授 (30362643)

Project Period (FY) 2016-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords非線形分子振動 / 磁性点群 / カラー対称性 / 共鳴振動 / 非線形振動 / 高調和振動 / 共鳴振動解析 / 振動対称性 / 群論
Outline of Final Research Achievements

This study investigates the symmetry of nonlinear normal mode vibrations of a two-dimensional molecule. Present numerical analysis revealed that nonlinearity of the system excites higher order harmonics in the normal mode vibration. Fourier spectrum analysis revealed that vibration symmetry of the higher harmonics can be classified on the basis of magnetic point group rather than the conventional irreducible representation of point group. This result indicates that magnetic point group is the appropriate framework for classification of normal mode vibration of solids.

Report

(3 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • Research Products

    (10 results)

All 2018 2017

All Journal Article (2 results) Presentation (8 results) (of which Invited: 1 results)

  • [Journal Article] 古典弾性理論における二つの近似とその弊害~固体の共鳴振動解析を通して~2017

    • Author(s)
      垂水竜一
    • Journal Title

      計算数理工学レビュー

      Volume: 2017年1号 Pages: 1-9

    • NAID

      40021333951

    • Related Report
      2016 Research-status Report
  • [Journal Article] 固体の共鳴振動理論の深化と展開2017

    • Author(s)
      垂水竜一
    • Journal Title

      学術の動向

      Volume: 22 Pages: 26-31

    • NAID

      130005712449

    • Related Report
      2016 Research-status Report
  • [Presentation] ひずみ勾配弾性理論を用いた共鳴振動現象のサイズ依存性解析2018

    • Author(s)
      木村 雄大,垂水 竜一,渋谷 陽二
    • Organizer
      日本機械学会関西支部第93期定時総会講演会
    • Related Report
      2017 Annual Research Report
  • [Presentation] ひずみ勾配弾性理論に現れる弾性定数テンソルの一般線形群の下での既約分解2017

    • Author(s)
      小林舜典, 垂水竜一, 渋谷陽二
    • Organizer
      日本物理学会春季大会
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2017-03-17
    • Related Report
      2016 Research-status Report
  • [Presentation] 二次元分子モデルの非線形共鳴振動とその対称性解析2017

    • Author(s)
      中村 隼一,垂水 竜一,渋谷 陽二
    • Organizer
      日本機械学会関西支部第92期定時総会講演会
    • Place of Presentation
      大阪大学吹田キャンパス
    • Year and Date
      2017-03-13
    • Related Report
      2016 Research-status Report
  • [Presentation] 非線形弾性体の共鳴振動とグリューナイゼン定数の推定2017

    • Author(s)
      垂水竜一, 渋谷陽二
    • Organizer
      日本物理学会春季大会
    • Related Report
      2017 Annual Research Report 2016 Research-status Report
  • [Presentation] ひずみ勾配弾性体のフォノン振動モードとサイズ効果2017

    • Author(s)
      木村雄大, 垂水竜一, 渋谷陽二
    • Organizer
      日本物理学会春季大会
    • Related Report
      2017 Annual Research Report 2016 Research-status Report
  • [Presentation] 二次元周期構造体の基準振動モードとサイズ効果2017

    • Author(s)
      木村雄大,垂水竜一,渋谷陽二
    • Organizer
      日本物理学会秋季大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 非線形分子振動に現れる高調和振動の対称性とその選択則2017

    • Author(s)
      垂水竜一,渋谷陽二
    • Organizer
      日本物理学会秋季大会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 古典弾性理論における二つの近似とその弊害~固体の共鳴振動解析を通して~2017

    • Author(s)
      垂水竜一
    • Organizer
      計算数理工学フォーラム
    • Place of Presentation
      大阪大学吹田キャンパス
    • Related Report
      2016 Research-status Report
    • Invited

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Published: 2016-04-21   Modified: 2019-03-29  

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