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A Study on the Nonlinear Normal Mode Vibration Using Adelphic Integral
Huinam Rhee,Jeong-Soo Kim 대한기계학회 2003 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.17 No.12
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.
Bryan’s Factor of a Hemispherical Resonator due to Coriolis Effect
Huinam Rhee(이희남),Sangjin Park(박상진),Sergii A. Sarapuloff(세르게이 사라플로프),Sunu Han(한순우),Jinho Park(박진호) 한국소음진동공학회 2014 한국소음진동공학회 학술대회논문집 Vol.2014 No.10
세차계수는 플랫폼의 각속도 혹은 회전각에 대한 공진기에 형성되는 탄성 정상파의 각속도 혹은 회전각의 비율로 정의된다. 본 논문에서는 코리올리 효과에 의한 반구형 공진기의 세차계수에 대한 연구를 레일리-리츠법과 라그랑지안 역학을 이용하여 수행하였으며 쉘의 중립면이 레일리 모드 변형을 한다는 조건을 적용하였고 계산 결과를 이전 연구자들의 결과들과 비교하였다. Precession coefficient is defined by the ratio of the angular rate or rotational angle of the standing wave formed in an elastic resonator with respect to that of the platform. In this paper the precession of a hemispherical resonator due to Coriolis’ effect is studied through Rayleigh-Ritz’s method and Lagrangian Mechanics when the resonator undergoes Rayleigh’s mode deformation. The calculation result was compared with studies by other researchers.
Analysis of the Thermo-Elastic Damping of a Beam-Type Resonator
Huinam Rhee(이희남),Junsung Park(박준성),Sergii A. Sarapuloff(세르게이 사라플로프),Soon Woo Han(한순우),Jin Ho Park(박진호) 한국소음진동공학회 2014 한국소음진동공학회 학술대회논문집 Vol.2014 No.10
This paper deals with the thermo-elastic damping (TED) due to the temperature change in a beam when it is in a resonant condition. Based on previous references, the analytical formulation for TED of a resonant thin beam was derived, and then TED was expressed as a function of the geometry of the beam, especially, its thickness. It was clearly shown that TED of a resonant beam is significantly varied for different thickness. Finally, the worst thickness of the beam has been identified in regard to the high-Q factor, and the result was compared to the finite element analysis.