2003 Fiscal Year Final Research Report Summary
Research on Reduced-order Nonlinear Modal Equations for Arbitrary Continuous Structures
| Project/Area Number |
14550207
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Dynamics/Control
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| Research Institution | HOKKAIDO UNIVERSITY |
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Principal Investigator |
KOBAYASHI Yukinori Hokkaido Univ., Grad.School of Eng., Assoc.Prof., 大学院・工学研究科, 助教授 (10186778)
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| Project Period (FY) |
2002 – 2003
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| Keywords | Nonlinear Vibration / Finite Element Method / Modal Equation / Modal Analysis / Continuous System |
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| Research Abstract |
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.
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