Proceedings of the Korean Society for Noise and Vibration Engineering Conference (한국소음진동공학회:학술대회논문집)
- 2001.11b
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- Pages.799-804
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- 2001
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- 1598-2548(pISSN)
A Study on the Nonlinear Normal Mode Vibration Using Adelphic Integral
Adelphic Integral을 이용한 비선형 정규모드 진동 해석
- Huinam Rhee (Dept.of Mechanical Automotive Engineering, Sunchon National University) ;
- Joo, Jae-Man ;
- Pak, Chol-Hui
- Published : 2001.11.01
Abstract
Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6th order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhotf-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.
Keywords
- Adelphic Integral;
- Nonlinear Normal Mode Vibration;
- Poincare Map;
- Hamiltonial;
- Action-Angle Variable;
- Birkhoff-Gustavson Canonical Transformation;
- Bifurcation;
- Internal Resonance
- 아델픽 적분;
- 비선형 정규 모드 진동;
- 푸앙카레 사상;
- 해밀토니안;
- 운동-각도 변수;
- 버크호프-구스타프슨 표준 변화;
- 분기;
- 내부공진;