Optimization of time-averaged quantities based on the second-order response analyses to arbitrary small-amplitude forced vibration

• Project/Area Number: 16K06157
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Dynamics/Control
• Research Institution: Setsunan University (2018-2019); Osaka University (2016-2017)
• Principal Investigator: ISHIDA Hideshi 摂南大学, 理工学部, 准教授 (80283737)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2017: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
• Keywords: 振動 / 最適化 / 時間平均量 / 大域最適解 / 非反復 / ノンパラメトリック / 熱対流 / ブシネ方程式系 / 機械力学・制御 / 微小振幅 / 漸近解 / 時間平均量最適化

Outline of Final Research Achievements

A perturbative expansion is obtained analytically that describes the response to an arbitrary small-amplitude periodic forced vibration around linearly stable steady solutions, providing the method to maximize or minimize time-averaged quantities categorized into inner-product type by optimizing for the complex field of vibrational sources. Applying this method to the thermal convection field in a square cavity, vibrational heat and vorticity sorces are firstly obtained that maximize or minimize the heat transfer rate, Nusselt number.

Academic Significance and Societal Importance of the Research Achievements

ダンパを導入するなどして無振動状態で安定静止状態を保つ工学的対象物は多い．このような対象に周期振動を加えた場合にある種の量の時間平均量を大域的に最大・最小化する振動源の分布を極めて短時間に求める手法を開発した．この手法は”無振動で安定静止"の条件さえ満足していればいいので，流体と構造物が相互作用して振動する場合の最適な機体の設計や，流体を離れて，ある都市部の建物群に最もダメージを与える地震動を特定するなど，多くの応用が考えられる．

Research Products

• [Journal Article] Global, nonparametric, noniterative optimization of time-averaged quantities under small, time-varying forcing: An application to a thermal convection field (2019)
  • Author(s): H. Ishida, S. Ihara, C. Okema, S. Yamada, and G. Kawahara
  • Journal Title: Numer. Heat Transfer, Part B Volume: 76 Issue: 4 Pages: 185-202
  • DOI: 10.1080/10407790.2019.1665436
  • Peer Reviewed
• [Presentation] 任意微小振幅強制振動下での大域的ノンパラメトリック時間平均量最適化－熱対流場への適用－ (2019)
  • Author(s): 芝田雄介，木飼和希，石田秀士
  • Organizer: 第５回摂南大学融合科学研究所講演会
• [Presentation] 微小振幅強制振動熱対流場における熱伝達率の時間平均量最適化 (2018)
  • Author(s): 井原詩帆，山田祥平，石田秀士，河原源太
  • Organizer: 日本機械学会関西学生会2017年度学生員卒業研究発表講演会
• [Presentation] 微小振幅強制振動下でのノンパラメトリック時間平均量最適化-熱対流場への適用- (2018)
  • Author(s): 石田秀士，井原詩帆，山田祥平，河原源太
  • Organizer: 日本機械学会関西支部 第93期定時総会講演会
• [Presentation] Non-parametric optimization of time-averaged quantities under small, time-varying forcing: an application to a thermal convection field (2017)
  • Author(s): H. Ishida, C. Okema, and G. Kawahara
  • Organizer: Optimization2017, Lisbon, Portugal
  • Int'l Joint Research