Development of Analytical Method on Low-computational-cost Nonlinear Vibrations of a Complex-shaped Thin Walled Plate with Dividing Segments

Research Project

Project/Area Number	20K04358
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Review Section	Basic Section 20010:Mechanics and mechatronics-related
Research Institution	Gunma University
Principal Investigator	Maruyama Shinichi 群馬大学, 大学院理工学府, 教授 (60344925)
Project Period (FY)	2020-04-01 – 2023-03-31
Project Status	Completed (Fiscal Year 2022)
Budget Amount *help	¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000) Fiscal Year 2022: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000) Fiscal Year 2021: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000) Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords	非線形振動 / 連続体の振動
Outline of Research at the Start	現在申請者らが検討を進めている，薄肉矩形板・円環板の線形振動解析を基に，一般形状区分での解析と，面内応力の解析が行えるように改良する．つぎに，与えられた面内境界条件の下で，たわみに伴う面内の伸縮による面内応力を，上述の面内応力解法を用いて，たわみに関する未知量の関数として表現し，これを面外方向の離散化運動方程式に導入することで，非線形振動解析法を定式化する．さらに，複雑形状を有する薄肉連続弾性体の非線形振動実験を行い，解析手法の検証を行う．
Outline of Final Research Achievements	Aiming at developing analytical method of nonlinear vibrations of complex-shaped flat and curved plates, a formulation is proposed in which the plates are divided into segments with relatively small number and the deflection and in-plane displacements in the segments are assumed with higher order differentiable functions. First, the analytical method previously proposed in which the plates are divided into segments with orthogonal shape is extended to that based on non-orthogonal shape to meet the analysis of complex-shaped plates. Furthermore, the method was also extended to the vibrations of shallow shell-panel in which in-plane displacement and lateral deflection is coupled. The analytical results were compared with existing exact solutions which verify the presented analysis.
Academic Significance and Societal Importance of the Research Achievements	極端な軽量化や微細化が進展する近年の機械要素において，各方向の変形が連成した複雑な振動応答の解析を，高精度かつ低コストで行うことは重要であり，その確立につながる成果が得られたものと言える．