• 한국소음진동공학회논문집
• /
• 제18권6호
• /
• pp.681-689
• /
• 2008

This paper is concerned with the free vibration analysis of a circular plate with an eccentric circular hole by the Independent coordinate coupling method(ICCM). It was proved in the previous study that the ICCM can accurately predict the natural frequencies and mode shapes of the annular plates and can also be used for the free vibration analysis of the simply-supported circular plate with an eccentric circular hole. In this study, the clamped and free boundary conditions were considered for the circular plate. The numerical results show that the ICCM can be used effectively for the free vibration problem of circular plate with an eccentric hole compared to the finite element method.

• 한국강구조학회 논문집
• /
• 제22권3호
• /
• pp.241-251
• /
• 2010

본 논문에서는 등분포 하중을 받는 등방성 환형 섹터판의 지배방정식에 대한 새로운 해석적 해가 3차원 극좌표계에서 개발된다. 4차의 편미분방정식 형태를 가지는 지배방정식은 레비 타입 시리즈 해에 대한 가정과 그 후속적인 수학적 처리를 통해 4차의 상미분방정식으로 전환된다. 전환된 상미분방정식의 특성방정식에 대한 실수 영역 및 복소수 영역의 해를 해석적으로 구한 후 제차 및 비제차 방정식의 각 해의 조합으로 최종적인 지배방정식의 해가 완성된다. 개발된 해의 수렴성 및 정확성을 보여주기 위해 다양한 경계조건 및 내부 중심 각도를 가지는 판에 대한 예제 해석을 수행하였고 그 결과를 다른 해석적 연구결과와 비교하였다. 또한 개발된 해의 정확성을 확인하기 위하여 유한요소 프로그램인 ABAQUS를 이용한 탄성해석을 추가로 수행하여 그 결과를 비교하였다. 제안된 해로부터 결정된 환형 섹터판의 변위 및 모멘트 값은 여타의 해석적 및 수치적 접근방법으로 구한 값들과 비교해 본 결과 매우 높은 수준에서 일치하고 있음이 확인되었다.

• 한국자동차공학회논문집
• /
• 제3권6호
• /
• pp.96-111
• /
• 1995

A bellows is a component installed in the automobile exhaust system to reduce the impact from an engine. It's stiffness has a great influence on the natural frequency of the system. Therefore, it must be designed to keep the specified stiffness that requires in the system. This study present the finite element analysis of U-typed bellows using a curved conical frustum element and the shape optimal design with specified stiffness. The finite element analysis is verified by comparing with the experimental results. In the shape optimal design, the weight is considered as the cost function. The specified stiffness from the system design is transformed to equality constraints. The formulation has inequality constraints imposed on the fatigue limit, the natural frequencies, the buckling load and the manufacturing conditions. A procedure for shape optimization adopts a thickness, a corrugation radius, and a length of annular plate as optimal design variables. The external loading conditions include the axial and lateral loads with a boundary condition fixed at an end of the bellows. The recursive quadratic programming algorithm is selected to solve the problem. The result are compared with the existing bellows, and the characteristics of the bellows is investigated through the optimal design process. The optimized shape of the bellows are expected to give quite a good guideline to the practical design.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2007년도 춘계학술대회논문집
• /
• pp.859-865
• /
• 2007

This paper presents a method to analyze the unbalance response of a high speed polygon mirror scanner motor supported by sintered bearing and flexible supporting structures by using the finite element method and the mode superposition method. The appropriate finite element equations for polygon mirror are described by rotating annular sector element using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. The rotating components except for the polygon mirror are modeled by Timoshenko beam element including the gyroscopic effect. The flexible supporting structures are modeled by using a 4-node tetrahedron element and 4-node shell element with rotational degrees of freedom. Finite element equations of each component of the polygon mirror scanner motor and the flexible supporting structures are consistently derived by satisfying the geometric compatibility in the internal boundary between each component. The rigid link constraints are also imposed at the interface area between sleeve and sintered bearing to describe the physical motion at this interface. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem by using the restarted Arnoldi iteration method. Unbalance responses in time and frequency domain are performed by superposing the eigenvalues and eigenvectors from the free vibration analysis. The validity of the proposed method is verified by comparing the simulated unbalance response with the experimental results. This research also shows that the flexibility of supporting structures plays an important role in determining the unbalance response of the polygon mirror scanner motor.

• 대한기계학회논문집A
• /
• 제26권9호
• /
• pp.1905-1913
• /
• 2002

Using the finite element method, this study investigates the dynamic time responses of a flexible spinning disk of which axis of rotation is misaligned with the axis of symmetry. The misalignment between the axes of symmetry and rotation is one of the major vibration sources in optical disk drives such as CD-ROM, CD-R, CD-RW and DVD drives. Based upon the Kirchhoff plate theory and the von-Karman strain theory, three coupled equations of motion for the misaligned disk are obtained: two of the equations are for the in-plane motion while the other is for the out-of-plane motion. After transforming these equations into two weak forms for the in-plane and out-of-plane motions, the weak forms are discretized by using newly defined annular sector finite elements. Applying the generalized-$\alpha$ time integration method to the discretized equations, the time responses and the displacement distributions are computed and then the effects of the misalign ment on the responses and the distributions are analyzed. The computation results show that the misalignment has an influence on the magnitudes of the in-plane displacements and it results in the amplitude modulation or the beat phenomenon in the time responses of the out-of-plane displacement.

• 한국소음진동공학회논문집
• /
• 제15권3호
• /
• pp.251-258
• /
• 2005

The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings (HDB) in an HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Reynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigen value problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2003년도 추계학술대회논문집
• /
• pp.572-578
• /
• 2003

The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings in a HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Raynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigenvalue problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

• 대한기계학회논문집A
• /
• 제27권4호
• /
• pp.601-607
• /
• 2003

The column type is used as the sensing element of the load cell to measure the large force in the range of 10$^4$~ 10$^{7}$ N. However. it is not easy to handle the load with large capacity due to its size. It is, therefore, necessary to design a compact load cell with a low aspect ratio. Thus this paper showed the characteristic evaluation of compact load cell with respect to the shape of supporting plate. The supporting plate of the load cell was an annular type with inner(D$_{i}$) and outer(D$_{o}$) diameters. Using the strain distribution obtained from FEM. the supporting plate was designed to get the stable output voltage of the load cell. The three designed supporting plates were manufactured, and the result of characteristic experiment of the load cell, using the 10 MN hydraulic force standard machine, was compared with FEM.M.M.

• Structural Engineering and Mechanics
• /
• 제65권5호
• /
• pp.523-533
• /
• 2018

In this study, the dynamic response of a functionally graded material (FGM) circular plate in contact with incompressible fluid under the harmonic load is investigated. Analysis of the plate is based on First-order Shear Deformation Plate Theory (FSDT). The governing equation of the oscillatory behavior of the fluid is obtained by solving Laplace equation and satisfying its boundary conditions. A new set of admissible functions, which satisfy both geometrical and natural boundary conditions, are developed for the free vibration analysis of moderately thick circular plate. The Chebyshev-Ritz Method is employed together with this set of admissible functions to determine the vibrational behaviors. The modal superposition approach is used to determine the dynamic response of the plate exposed to harmonic loading. Numerical results of the force vibrations and the effects of the different geometrical parameters on the dynamic response of the plate are investigated. Finally, the results of this research in the limit case are compared and validated with the results of other researches and finite element model (FEM).

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2006년도 춘계학술대회논문집
• /
• pp.660-665
• /
• 2006

This paper presents a finite element method to analyze the free and forced vibration of a hard disk drive (HDD) considering the flexibility of a spinning disk-spindle with fluid dynamic bearings (FDBs), an actuator with pivot bearings, an air bearing between head-disk interface and the base with complicated geometry. Finite element equation of each component is consistently derived with the satisfaction of the geometric compatibility of the internal boundary between each component. The spinning disk, hub and FDBs are modeled by annular sector elements, beam elements and stiffness and damping elements, respectively. The actuator am, E-block, suspension and base plate are modeled by tetrahedral elements. The pivot bearing in the actuator and the air bearing between head-disk interfaces are modeled by the stiffness element with five degrees of freedom and the axial stiffness, respectively. A global matrix equation obtained by assembling the finite element equations of each substructure is transformed to a state-space matrix-vector equation, and both damped natural frequencies and modal damping ratios are calculated by solving the associated eigenvalue problem with the restarted Arnoldi iteration method. Modal and shock testing are performed to show that the proposed method well predicts the vibration characteristics of a HDD.