• 대한기계학회논문집
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• 제17권7호
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• pp.1719-1730
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• 1993

This paper presents the theoretical natural frequencies of out-of-plane deformable ring based on the variables such as out-of-plane deflection, torsional rotation and shear rotation. Based on the same variables, a finite element eigen analysis is carried out by using the $C^0$-continuous, isoparametric element which has three nodes per element and three degrees-of-freedom at each node. Numerical experiments are peformed to find the integration scheme which produces accurate natural frequencies, natural modes and correct rigid body motion. The uniformly reduced integration and the selective reduced integration give more accurate numerical frequencies than the uniformly full integration, but the uniformly reduced integration produces incorrect rigid body motion while selective reduced integration does correct one. Therefore, the ring element based on the three variables which employes selective reduced integration is recommended to avoid spurious modes, to alleviate the error due to shear locking and to produce correct rigid body motion, simultaneously.

• 대한기계학회논문집A
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• 제27권1호
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• pp.42-47
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• 2003

Nonlinear models for a thin ring rotating at a constant speed are developed. The geometric nonlinearity of displacements is considered by adopting the Lagrange strain theory for the circumferential strain. By using Hamilton’s principle, the coupled nonlinear partial differential equations are derived, which describe the out-of-plane and in-plane bending, extensional and torsional motions. The natural frequencies are calculated from the linearized equations at various rotational speeds. Finally, the computation results from the nonlinear models are compared with those from a linear model. Based on the comparison, this study recommends which model is appropriate to describe the behavior of the rotating ring.

• 한국철도학회논문집
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• 제15권6호
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• pp.588-596
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• 2012

이 논문은 두꺼운 디스크의 면외 고유 진동을 유한 요소법을 사용하여 회전 관성 및 횡 전단 변형의 효과를 포함하면서 단순하고 효율적으로 정밀하게 해석할 수 있는 새로운 준-해석적 환상 민드린 평판 요소를 제시한다. 환상 민드린 평판의 평형 방정식의 정확한 해인 정적 변형 모드를 사용하여 요소의 보간 함수, 강성 및 질량 행렬은 절 직경 수에 대하여 유도되며, 이와 같은 요소는 면외 강체 운동을 정확하게 표현할 수 있고 전단 잠김이 없다. 제시된 요소를 적용하여 동심 링으로 지지되거나 지지되지 않은 균일 디스크 및 다단 디스크의 고유진동수를 해석하고, 그 결과를 선행 연구의 이론적 결과 또는 2차원 쉘 요소를 사용하여 얻어진 유한요소 해석 결과와 비교하여 제시된 요소의 수렴성 및 정확성을 조사하였다.

• 한국소음진동공학회논문집
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• 제16권1호
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• pp.57-65
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• 2006

In this paper, we present the principle of virtual work, from which the exact non-linear equations of motion of a rotating ring can be derived, by using the theory of finite deformation. For a thin ring of which the effect of variation in curvature across the cross-section is neglected, the radial displacement and the extensional stress are determined from the principle of virtual work at the steady state where the ring is rotating with a constant angular velocity. And also we formulate systematically the governing equations concerned to the in-plane vibrations and the out-of-plane vibrations at the disturbed state by using the principle of virtual work which is expressed with the disturbed displacements about the steady state. The formulated governing equations are classified by four models along the cases of considering or neglecting all or partly the secondary effects of flexural shear, rotary inertia, circumferential extension, and twist inertia. The natural vibrations of thin rings are analyzed, and its results are compared and discussed.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 추계학술대회논문집
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• pp.585-592
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• 2005

In this paper, we present the principle of virtual work, from which the exact non-linear equations of motion of a rotating ring can be derived, by using the theory of finite deformation For a thin ring of which the effect of variation in curvature across the cross-section is neglected, the radial displacement and the extensional stress are determined from the principle of virtual work at the steady state where the ring is rotating with a constant angular velocity. And also we formulate systematically the governing equations concerned to the in-plane vibrations and the out-of-plane vibrations at the disturbed state by using the principle of virtual work which is expressed with the disturbed displacements about the steady state. The formulated governing equations are classified by four models along the cases of considering or neglecting all or partly the secondary effects of flexural shear, rotary inertia, circumferential extension, and twist inertia. The natural vibrations of thin rings are analyzed, and its results are compared and discussed.