• Journal of Mechanical Science and Technology
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• 제17권12호
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• pp.1922-1927
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• 2003

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6$\^$th/ 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 Birkhoff-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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.799-804
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• 2001

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.

• 소음진동
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• 제9권1호
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• pp.196-205
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• 1999

6승의 비선형 항을 가지는 두개의 질량으로 구성된 비선형 해밀톤계에 대해서, 비선형 정규모드인 주기운동의 존재성, 분기현상 및 궤도 안정성을 연구하였다. 운동방정식의 직접적분을 통해 4차원 위상공간에서의 운동궤적을 2차원 면으로 투영하는 푸앙카레 사상을 구하였고, 또한 버크 호프-구스타프슨 표준 변환을 통해 구한 운동적분을 이용하여 에너지가 작을때 푸앙카레 사상에 나타나는 불변 곡선들의 해석적인 표현을 유도하였다. 본 논문에서 연구한 진동계는 비선형 계수의 값에 따라 2개 또는 4개의 비선형 정규모드를 가짐이 밝혀졌다. 푸앙카레 사상은, 분기된 모드는 안정하고, 원래의 모드는 안정한 상태에서 불안정한 상태로 변한다는 것을 분명하게 보여주었다.