• 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.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.55-60
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• 2011

The aim of the paper is to apply Homotopy Perturbation Method (HPM) for the solution of a nonlinear fractional differential equation. Finally, the solution obtained by the Homotopy perturbation method has been numerically evaluated and presented in the form of tables and then compared with those obtained by truncated series method. A good agreement of the results is observed.

• Advances in concrete construction
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• v.9 no.3
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• pp.267-278
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• 2020

This paper reports on the result of an experimental investigation carried out to study the compressive strength and sorptivity properties of blended cement concrete exposed to 5% and 10% MgSO₄ solution using fly ash (FA) and silpozz. Usually in sulphate environment the minimum grade of concrete is M30 and the mix design is done for target mean strength of 39 MPa. Silpozz is manufactured by burning of agro-waste rice husk in designed furnace in between 600° to 700℃ which is one of the main agricultural residues obtained from the outer covering of rice grains during the milling process. There are four mix series taken with control mix. The control mix made 0% replacement of FA and silpozz with Ordinary Portland Cement (OPC). The first mix series made 0% FA and 10-30% replacement of silpozz with OPC. The second mix series made with 10% FA and 10-40% replacement of silpozz with OPC. The third mix series made 20% FA and 10-30% replacement of silpozz with OPC and the fourth mix series made 30% FA and 10-20% silpozz replaced with OPC. The samples (cubes) are prepared and cured in normal water and 5% and 10% MgSO₄ solution for 7, 28 and 90 days. The studied parameters are compressive strength and strength deterioration factor (SDF) for 7, 28 and 90 days. The water absorption and sorptivity tests have been done after 28 days of normal water and magnesium sulphate solution curing. The investigation reflects that the blended cement concrete incorporating FA and silpozz showing better resistance against MgSO₄ solution when compared to normal water curing (NWC) samples.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.55-63
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• 2013

In this paper, a general technique is proposed for solving a system of fourth-order boundary value problems. The solution is given in the form of series and its approximate solution is obtained by truncating the series. Advantages of the method are that the representation of exact solution is obtained in a new reproducing kernel Hilbert space and accuracy of numerical computation is higher. Numerical results show that the method employed in the paper is valid. Numerical evidence is presented to show the applicability and superiority of the new method.

• 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.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.157-166
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• 2006

In order to model blending surfaces with curvature continuity, in this paper we apply sixth order partial differential equations (PDEs), which are solved with a composite power series based method. The proposed composite power series based approach meets boundary conditions exactly, minimises the errors of the PDEs, and creates almost as accurate blending surfaces as those from the closed form solution that is the most accurate but achievable only for some simple blending problems. Since only a few unknown constants are involved, the proposed method is comparable with the closed form solution in terms of computational efficiency. Moreover, it can be used to construct 3- or 4-sided patches through the satisfaction of continuities along all edges of the patches. Therefore, the developed method is simpler and more efficient than numerical methods, more powerful than the analytical methods, and can be implemented into an effective tool for the generation and manipulation of complex free-form surfaces.

• Structural Engineering and Mechanics
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• v.31 no.6
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• pp.663-678
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• 2009

An exact solution is obtained for forced torsional vibration of a finite class 622 piezoelectric hollow cylinder with free-free ends subjected to dynamic shearing stress and time dependent electric potential at both internal and external surfaces. The solution is first expanded in axial direction with trigonometric series and the governing equations for the new variables about radial coordinate r and time t are derived with the aid of Fourier series expansion technique. By means of the superposition method and the separation of variables technique, the solution for torsional vibration is finally obtained. Natural frequencies and the transient torsional responses for finite class 622 piezoelectric hollow cylinder with free-free ends are computed and illustrated.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.29 no.1
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• pp.7-14
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• 2017

This study carried out a numerical analysis of the effects of hot waste water supply on the performance of a Type II absorption heat pump. There are two types of hot waste water supply, regular series flow and reverse series flow. Also it investigated the interaction between each type of flow and heat exchange solutions. As the effectiveness of heat exchange solutions increase, the steam generation and (COP) increase as well. If the effectiveness of a heat exchange solution is lower than 0.566, the steam generation rate of the reverse flow is lower than that of the regular series flow. A high effectiveness of heat exchange solution is therefore required to make a larger amount of steam in reverse series flow than with ordinary series flow. The COP difference between the two types of flow decreases with the increasing effectiveness of the heat exchange solution. Thus, a reverse flow type absorption heat pump can match the high steam generation rate and COP of the ordinary flow type when a highly effective heat exchange solution is applied.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.4B
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• pp.413-419
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• 2008

In this study, we develop analytical solutions for long waves propagating over several types of axis-symmetric topographies where the water depth varies in an arbitrary power of radial distance. The first type is a cylindrical island mounted on a shoal. The second type is a circular island. To get the solution, the methods of separation of variables, Taylor series expansion and Frobenius series are used. Developed analytical solutions are validated by comparing with previously developed analytical solutions. We also investigate various cases with different incident wave periods, radii of the shoal, and the powers of radial distance.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.583-593
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• 2022

Lienard's equations are important nonlinear differential equations with application in many areas of applied mathematics. In the present article, a new approach known as the modified fractional Taylor series method (MFTSM) is proposed to solve the nonlinear fractional Lienard equations with Caputo fractional derivatives, and the convergence of this method is established. Numerical examples are given to verify our theoretical results and to illustrate the accuracy and effectiveness of the method. The results obtained show the reliability and efficiency of the MFTSM, suggesting that it can be used to solve other types of nonlinear fractional differential equations that arise in modeling different physical problems.