• Proceedings of the KSR Conference
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• 2008.11b
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• pp.1379-1388
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• 2008

In this paper, we present the equations of motion by which the natural vibration of a rotating annular disk can be accurately analyzed. These equations are derived from the theory of finite deformation and the principle of virtual work. The radial displacements of annular disk which is rotating at constant angular velocity are determined by non-linear equations formulated using 1-dimensional finite elements in radial direction. The equations of the in-plane vibrations at disturbed state are also formulated using 1-dimensional finite elements in radial direction along the number of nodal diameters. They are expressed as in functions of the radial displacements at the steady state and the disturbed displacements about the steady state. In-plane static deformation modes of the annular disk are used as the interpolation functions of 1-dimensional finite elements in radial direction. The natural vibrations of an annular disk with different boundary conditions are analyzed by using the presented model and the 3-dimensional finite element model to verify accuracy of the presented equations of motion. Its results are compared and discussed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.2
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• pp.208-216
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• 2009

In this paper, we present the equations of motion by which the natural vibration of a rotating annular disk can be analyzed accurately. These equations are derived from the theory of finite deformation and the principle of virtual work. The radial displacements of annular disk at the steady state where the disk is rotating at a constant angular velocity are determined by non-linear static equations formulated with 1-dimensional finite elements in radial direction. The linearlized equations of the in-plane vibrations at the disturbed state are also formulated with 1-dimensional finite elements in radial direction along the number of nodal diameters. They are expressed as in functions of the radial displacements at the steady state and the disturbed displacements about the steady state. In-plane static deformation modes of an annular disk are used as the displacement functions for the interpolation functions of the 1-dimensional finite elements. The natural vibrations of an annular disk with different boundary conditions are analyzed by using the presented model and the 3-dimensional finite element model to verify accuracy of the presented equations of motion. Its results are compared and discussed.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.515-528
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• 2006

This article presents a unified analytical solution for the analysis of thermal deformations and stresses in elastic annular disks with arbitrary cross-sections of continuously variable thickness. The annular disk is assumed to be under steady heat flow conditions, in which the inner surface of the annular disk is at an initial temperature and the outer surface at zero temperature. The governing second-order differential equation is derived from the basic equations of the thermal annular disks and solved with the aid of some hypergeometric functions. Numerical results for thermal stresses and displacement are given for various annular disks. These disks include annular disks of thickness profiles in the form of general parabolic and exponential functions. Additional annular disks with nonlinearly variable thickness and uniform thickness are also included.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.6
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• pp.560-568
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• 2009

Modal vibration characteristics of a thin annular disk containing narrow radial slots are studied numerically and experimentally. Existing analytical solution is examined based on these results revealing that it can not precisely predict eigenvalues of the disk with slots since it does not accurately consider change in the vibration modes and change in strain energy density distributions due to the slots. Parametric study on slot length found that distortions in the mode shape as well as changes in the corresponding natural frequencies are proportional to the slot length. Consequently, errors in the calculated eigenvalues are also proportional to the slot length and accurate data can not be obtained with existing analytical solution above a certain level of slot length. Same phenomena can be observed in both free-free disk and fixed-free disk.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.12
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• pp.1338-1346
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• 2009

We present a one-dimensional annular plate element with which the in-plane vibration of full disks can be analyzed efficiently and accurately by using the FEM. Its elementary mass matrix and stiffness matrix are derived, respectively, from the virtual work by effective forces and the virtual strain energy. The static deformation modes obtained from an integration of the differential equilibrium equations of the annular plate are used as interpolation functions of the one-dimensional annular plate element. The in-plane natural vibration characteristics of a 2-step full disk and a uniform full disk are analysed. Its results are compared with the results obtained by utilizing two-dimensional 8-node quadrilateral plane elements and cyclic symmetry of the disk. And also, by comparing with the theoretical results of previous researchers, the efficiency and accuracy of the presented element are verified.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.6
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• pp.843-850
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• 1990

A numerical method is presented for determining the static charge distribution and the capacitance of a round disk capacitor. In the employed numerical scheme annular patch subdomains are introduced to reduce the matrix size and to mprove the accuracy of the numerical calculations. The method of moments is utilized to calculate the charge distribution, and the capacitance and equipotential lines are also found from the numerically computed charge distributions. To show the validity of the results the proposed method is applied to the round disk and the dielectric filled capacitor.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.4 s.97
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• pp.412-420
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• 2005

This article proposes analytical solutions for sound radiation from radial vibration modes of a thick annular disk. Structural eigensolutions are calculated using the transfer matrix method. The far-field sound pressure distribution is obtained using two alternate methods. In the first method, pressure is calculated using the Rayleigh integral technique. The second method treats sound radiating radial surfaces as cylindrical radiators of finite length. The Sinc function approach is employed for calculations. Acoustic powers and radiation efficiencies of radial modes are also determined from the far-field sound pressure calculations. Analytical predictions match well with measured data as well as computational results from a finite element code in terms of structural eigensolutions and from a boundary element code in terms of sound pressure, directivity etc.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.12
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• pp.1853-1860
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• 2001

Characteristics of fluid flow and heat transfer in a tube with disk and annular baffle for heat exchanger of condensing boiler was numerically studied. The STAR-CD code was used to solve the governing equations and the temperature and flow fields were investigated. The interval between tube and annular baffle, height and diameter of baffle were selected as important design parameters, and the effects of these parameters on heat transfer and fluid flow were studied. As a result, in the case of with interval, the pressure was decreased, but heat transfer was increased. Heat transfer was slowly increased as the size of disk and annular baffle were increased and the distance between baffles were decreased. The pressure drop was rapidly changed fur diameter and size of disk and annular baffle. In addition, it was desirable that optimal conditions to design heat exchanger were about B$\_$a/R=0.5, L/R=1.

• Proceedings of the KSME Conference
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• 2001.06d
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• pp.71-78
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• 2001

It was numerically studied that characteristics of fluid flow and heat transfer in a tube with disk and annular baffle for heat exchanger of condensing boiler. Using a finite volume technique and CFD code, STAR-CD, the governing equations were solved and the temperature and flow fields were investigated. The interval between tube and annular baffle, height and diameter of baffle were selected as important design parameters, and the effects of these parameters on heat transfer and fluid flow were studied. As a result, in the case of with interval, the pressure was decreased but heat transfer was increased. Also heat transfer was slowly increased as the size of disk and annular baffle were increased and the distance between baffles were decreased.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1649-1654
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• 2004

The near field structures of an under-expanded, dual, coaxial, jets issuing from the coaxial nozzles with four different geometries are visualized by using a shadowgraph optical method. Experiments are conducted to investigate the effects of the nozzle-lip thickness, secondary stream thickness, the nozzle pressure ratio and the secondary swirl stream on the characteristics of under-expanded jets. The results show that the presence of secondary annular swirling stream causes the Mach disk to move further downstream and increases its diameter, which decreases with a decrease in the nozzle-lip thickness. The secondary stream thickness has an influence on the location of an annular shock wave.