• Journal of Magnetics
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• v.18 no.2
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• pp.130-134
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• 2013

Most electrical machines like motor, generator and transformer are symmetric in terms of magnetic field distribution and mechanical structure. In order to analyze these problems effectively, many coupling techniques have been introduced. This paper deals with a coupling scheme for open boundary problem of symmetric and periodic structure. It couples an analytical solution of Fourier series expansion with the standard finite element method. The analytical solution is derived for the magnetic field in the outside of the boundary, and the finite element method is for the magnetic field in the inside with source current and magnetic materials. The main advantage of the proposed method is that it retains sparsity and symmetry of system matrix like the standard FEM and it can also be easily applied to symmetric and periodic problems. Also, unknowns of finite elements at the boundary are coupled with Fourier series coefficients. The boundary conditions are used to derive a coupled system equation expressed in matrix form. The proposed algorithm is validated using a test model of a bush bar for the power supply. And the each result is compared with analytical solution respectively.

• Structural Engineering and Mechanics
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• v.16 no.6
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• pp.655-674
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• 2003

Investigated in this study are the natural vibration characteristics of the coaxial cylindrical shells coupled with a fluid. Theoretical method is developed to find the natural frequencies of the shell using the finite Fourier series expansion, and their results are compared with those of finite element method to verify the validation of the method developed. The effect of the fluid-filled annulus and the boundary conditions on the modal characteristics of the coaxial shells is investigated using a finite element modeling.

• Structural Engineering and Mechanics
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• v.8 no.4
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• pp.343-360
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• 1999

This work applies a structural analysis method based on an analytical solution from the Fourier series which transforms a half-range cosine expansion into a static solution involving plated structures. Two sub-matrices of in-plane and plate-bending problems are also formulated and coupled with the prescribed boundary conditions for these variables, thereby providing a convenient basis for a numerical solution. In addition, the plate connection are introduced by describing the connection between common boundary continuity and equilibrium. Moreover, a simple computation scheme is proposed. Numerical results are then compared with finite element results, demonstrating the numerical scheme's versatility and accuracy.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.908-913
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• 2002

An analytical study is presented on the hydroelastic vibration of two rectangular identical plates coupled with a bounded fluid by using the finite Fourier series expansion method. It is observed that the two contrastive modes, the so called the out-of-phase and in-phase modes appear. The proposed analytical method is verified by observing a good agreement to three dimensional finite element analysis results. All natural frequency of the in-phase modes can be predicted well by the combination of the dry beam modes. The theoretical prediction for the out-of-phase mode can be improved by using the polynomial functions satisfying the plate boundary conditions and fluid volume conservation instead of using dry beam modes.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.921-925
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• 2003

An analytical method for the free vibration of single circular plate submerged in a fluid-filled rigid cylindrical vessel was developed by the Rayleigh-Ritz method based on the Fourier-Bessel series expansion. It was assumed that the plate is clamped at an offcentered location of the cylinder, and the non-viscous incompressible fluid contained in the cylinder is bisected by the plate. It was found that the theoretical results can predict well the fluid-coupled natural frequencies with excellent accuracy comparing with the finite element analysis results. The offcentered distance effect on the natural frequencies was also observed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.9
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• pp.439-453
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• 2001

This study deals with the free vibration of two identical circular plates coupled with a bounded fluid. An analytical method based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method is suggested. In the theory, it is assumed that the ideal fluid in a rigid cylindrical container and the two plates are clamped along the plate edges. The proposed method is verified by the finite element analysis using commercial program with a good accuracy. Two transverse vibration modes, namely in-phase and out-of-phase, are observed alternately in the fluid-coupled system when the number of nodal circles increases for the fixed nodal diameter. The effect of gap between the plates on the fluid-coupled natural frequencies sis also investigated.

• Proceedings of the KIEE Conference
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• 1998.07a
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• pp.64-66
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• 1998

This paper presents a new efficient method for transient analysis in magnetodynamic systems of linear eddy current problems. This mehtod employs the Fourier transform and the high-order frequency sensitivity of harmonic finite element method. By taking into account the time-constant of magnetodynamic system, the Fourier integral of continuous frequency is converted into the Fourier series of discrete frequency. And with the results of Fourier series expansion of converted input wave form, the responses of each sinusoids is superposed to give the total response of the magnetodynamic systems. But, if the frequency band of input wave form is broad, it takes long computational time since all responses for each sinusoids must be calculated. Therefore, the high-order frequency sensitivity method is employed to estimate the response variation to frequency. The proposed algorithm is applied to an induction heating system to validate its numerical efficiency.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.2
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• pp.150-160
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• 2002

The free vibration characteristics of the triple cylindrical shells filled with fluid are investigated. The triple cylindrical shells are filled with compressible fluid. The boundary condition is clamped at both ends. Analytical method is developed to evaluate natural frequencies of triple cylindrical shells using Sanders' shell theory and courier series expansion by Stokes' transformation. Their results are compared with those of finite element method to verify the validation of the method developed. The modal characteristics of shells filled with fluid at region 1, 2 and 3 are evaluated.

• Structural Engineering and Mechanics
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• v.21 no.2
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• pp.169-184
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• 2005

This study deals with the free vibration of a circular plate in contact with a fluid; submerged in fluid, beneath fluid or on fluid. An analytical method based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method is suggested. The proposed method is verified by the finite element analysis using commercial program with a good accuracy. The normalized natural frequencies are obtained in order to estimate the relative added mass effect of fluid on each vibration mode of the plate. Also, the location of plate coupled with fluid and the cases of free and bounded fluid surface are studied for the effect on the vibration characteristics.

• Journal of Mechanical Science and Technology
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• v.17 no.9
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• pp.1297-1315
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• 2003

This study deals with the free vibration of two identical circular plates coupled with a bounded or unbounded fluid. An analytical method based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method is suggested. The proposed method is verified by the finite element analysis using commercial program with a good accuracy The case of bounded or unbounded fluid is studied for the effect on the vibration characteristics of two circular plates. Also, the effect of gap between the plates on the fluid-coupled natural frequencies is investigated.