Research on Reduced-order Nonlinear Modal Equations for Arbitrary Continuous Structures

任意连续结构降阶非线性模态方程研究

• 批准号: 14550207
• 负责人: KOBAYASHI Yukinori
• 金额: $ 2.11万
• 依托单位: HOKKAIDO UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14550207/
• 关键词: Nonlinear Vibration; Finite Element Method; Modal Equation; Modal Analysis; Continuous System

Procedures to derive reduced-order nonlinear modal equations for various continuous structures have been studied in this research. Nonlinear finite element formulation was derived by the principle of virtual work taking into account geometrical nonlinearity. Reduced-order model was derived by transforming the equations of motion from the physical coordinates to the modal coordinates. Pseudo mode vectors were determined by applying the Newton-Raphson method to an approximated nonlinear finite element equation. Modal analysis is applied to the nonlinear finite element equation by using non-classical mode vectors obtained by the finite element analysis. Present method was applied to a beam supported by a spring and a curved beam. Nonlinear modal equations of them were derived by using only a few mode vectors, and numerical results for the fundamental out-of-plane mode and an internal resonance showed good agreement with those presented in other papers. In the case of the curved beam, asymmetry of its deformation with respect to the neutral axis was taken into consideration to determine the mode vectors. Computational time of this method is very shorter than that of any other methods, and the present method maintains enough accuracy. In this study, a procedure was also proposed to determine the coefficient of nonlinear term of the modal equation by using numerical results of commercial finite element software. Validity of the procedure was verified by the numerical results on the first and third modes of a clamped beam.

本文研究了各种连续结构的降阶非线性模态方程的推导方法。采用虚功原理推导了考虑几何非线性的非线性有限元列式。通过将运动方程从物理坐标系转换到模态坐标系，得到了系统的降阶模型。伪模态向量通过将Newton-Raphson方法应用于近似的非线性有限元方程来确定。模态分析应用于非线性有限元方程，通过使用非经典模态向量得到的有限元分析。本文的方法被应用到一个由弹簧支撑的梁和一个曲梁。仅用少量模态向量就导出了它们的非线性模态方程，对基本离面模态和内共振的数值计算结果与文献中的结果吻合较好。在曲梁的情况下，考虑其变形相对于中性轴的不对称性来确定模态向量。该方法的计算时间比其他方法都要短，而且保持了足够的精度。本文还提出了一种利用商用有限元软件的数值计算结果来确定模态方程中非线性项系数的方法。通过对固支梁一阶和三阶模态的数值计算，验证了该方法的有效性。

项目成果

Harada, A., Kobayashi, Y., Yamada G., Nagaishi, M.: "Reduced-Order Nonlinear Modal Equations of Curved Beams by using Non-classical Mode"Proc.JSME Dynamics and Design Conf.. Paper No.336(CD-ROM). 1-6 (2003)

Harada, A.、Kobayashi, Y.、Yamada G.、Nagaishi, M.：“使用非经典模态的弯曲梁的降阶非线性模态方程”Proc.JSME 动力学与设计会议.论文第 336 号（

Harada, A., Kobayashi, Y., Yamada G.: "Reduced-order Nonlinear Modal Equations of PlatesBased on the Finite Element Method"Proc.Eighth Int.Conf.on Recent Advances in Structural Dynamics. (CD-ROM)(Paper No.19). 1-10 (2003)

Harada, A.、Kobayashi, Y.、Yamada G.：“基于有限元方法的板的降阶非线性模态方程”Proc.Eighth Int.Conf.on Contemporary Advances in Structural Dynamics。

小林幸徳, 原田晃, 山田元, 中林恵市: "ばね支持を有するはりの非線形振動解析"日本機械学会機械力学・計測制御講演会CD-ROM論文集. (Paper No.335). 1-6 (2003)

Yukinori Kobayashi、Akira Harada、Hajime Yamada、Keiichi Nakabayashi：“带有弹簧支撑的梁的非线性振动分析”日本机械工程学会机械动力学和仪器控制会议论文集 CD-ROM（论文第 335 号）。 6（2003）

Harada, A., Kobayashi, Y., Yamada G.: "Reduced-order Nonlinear Modal Equations of Plates Based on the Finite Element Method"Proc.Eighth International Conference on Recent Advances in Structural Dynamics. (CD-ROM). 1-10(Paper No.19) (2003)

Harada, A.、Kobayashi, Y.、Yamada G.：“基于有限元方法的板的降阶非线性模态方程”Proc.第八届结构动力学最新进展国际会议。

小林幸徳, 原田晃, 山田 元, 中林恵市: "ばね支持を有するはりの非線形振動解析"日本機械学会機械力学・計測制御講演会CD-ROM論文集. 1-6(Paper No.335) (2003)

Yukinori Kobayashi、Akira Harada、Hajime Yamada、Keiichi Nakabayashi：《带有弹簧支撑的梁的非线性振动分析》日本机械工程学会会议记录、机械动力学和仪器控制会议 CD-ROM 会议记录 1-6（论文集 1-6） 335) (2003)