• Title, Summary, Keyword: Double Fourier series

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On Classical Studies for Summability and Convergence of Double Fourier Series (이중 푸리에 급수의 총합가능성과 수렴성에 대한 고전적인 연구들에 관하여)

  • Lee, Jung Oh
    • Journal for History of Mathematics
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    • v.27 no.4
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    • pp.285-297
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    • 2014
  • G. H. Hardy laid the foundation of classical studies on double Fourier series at the beginning of the 20th century. In this paper we are concerned not only with Fourier series but more generally with trigonometric series. We consider Norlund means and Cesaro summation method for double Fourier Series. In section 2, we investigate the classical results on the summability and the convergence of double Fourier series from G. H. Hardy to P. Sjolin in the mid-20th century. This study concerns with the $L^1(T^2)$-convergence of double Fourier series fundamentally. In conclusion, there are the features of the classical results by comparing and reinterpreting the theorems about double Fourier series mutually.

On Lp(T2)-Convergence and Móricz (Lp(T2)-수렴성과 모리츠에 관하여)

  • LEE, Jung Oh
    • Journal for History of Mathematics
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    • v.28 no.6
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    • pp.321-332
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    • 2015
  • This paper is concerned with the convergence of double trigonometric series and Fourier series. Since the beginning of the 20th century, many authors have studied on those series. Also, Ferenc $M{\acute{o}}ricz$ has studied the convergence of double trigonometric series and double Fourier series so far. We consider $L^p(T^2)$-convergence results focused on the Ferenc $M{\acute{o}}ricz^{\prime}s$ studies from the second half of the 20th century up to now. In section 2, we reintroduce some of Ferenc $M{\acute{o}}ricz^{\prime}s$ remarkable theorems. Also we investigate his several important results. In conclusion, we investigate his research trends and the simple minor genealogy from J. B. Joseph Fourier to Ferenc $M{\acute{o}}ricz$. In addition, we present the research minor lineage of his study on $L^p(T^2)$-convergence.

Double Fourier Sine Series Method for The Free Vibration of a Rectangular Plate (이중 사인 시리즈법에 의한 직사각형 평판의 자유 진동해석)

  • 윤종욱;이장무
    • Journal of KSNVE
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    • v.6 no.6
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    • pp.771-779
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    • 1996
  • In this paper, double Fourier sine series is used as a modal displacement functions of a rectangular plate and applied to the free vibration analysis of a rectangular plate under various boundary conditions. The method of stationary potential energy is used to obtain the modal displacements of a plate. To enhance the flexibility of the double Fourier sine series, Lagrangian multipliers are utilized to match the geometric boundary conditions, and Stokes' transformation is used to handle the displacements that are not satisfied by the double Fourier sine series. The frequency parameters and mode shapes obtained by the present method are compared with those obtained by MSC/NASTRAN and other analysis.

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Harmonic Analysis of a Modular Multilevel Converter Using Double Fourier Series

  • Quach, Ngoc-Thinh;Chae, Sang Heon;Ahn, Jin Hong;Kim, Eel-Hwan
    • Journal of Electrical Engineering and Technology
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    • v.13 no.1
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    • pp.298-306
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    • 2018
  • This paper presents a harmonic analysis of the modular multilevel converter (MMC) using a double Fourier series (DFS) algorithm. First, the application of DFS for harmonic calculation in the MMC is made by considering the effect of arm inductor. The analytical results are then confirmed by comparing with the simulation results of using the fast Fourier transform (FFT) algorithm. Finally, distribution of harmonics and total harmonic distortion (THD) in the MMC will be analyzed in three cases: harmonics versus number of levels of MMC, harmonics versus total switching frequency and harmonics versus modulation index. The simulation results are performed in the PSCAD/EMTDC simulation program in order to verify the analytical results obtained by Matlab programming.

An Analysis of the Vibrational Modes for a Rectangular Plate by Using the Double Fourier Sine Series Method (이중 사인 시리즈법에 의한 직사각형 평판의 진동모드 해석)

  • 고영준;남효덕;장호경
    • The Journal of the Acoustical Society of Korea
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    • v.18 no.7
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    • pp.39-44
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    • 1999
  • An analysis of the frequency parameters and vibrational modes is described for a rectangular plate. Double Fourier sine series is used as a modal displacement functions of a rectangular plate and applied to the free vibration analysis of a rectangular plate under various boundary conditions. The frequency parameters obtained by the double Fourier sine series method are compared with those obtained by the theory of finite element method and Ritz method. Frequency parameters are presented for the various aspect ratios for plate. The first four modal shapes for the rectangular plate under various boundary conditions are accurately described.

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Single-Phase Multilevel PWM Inverter Based on H-bridge and its Harmonics Analysis

  • Choi, Woo-Seok;Nam, Hae-Kon;Park, Sung-Jun
    • Journal of Power Electronics
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    • v.15 no.5
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    • pp.1227-1234
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    • 2015
  • The efficient electric power demand management in electric power supply industry is currently being changed by distributed generation. Meanwhile, small-scale distributed generation systems using renewable energy are being constructed worldwide. Several small-scale renewable distributed generation systems, which can supply electricity to the grid at peak load of the grid as per policy such as demand response programs, could help in the stability of the electric power demand management. In this case, the power quality of the small-scale renewable distributed generation system is more significant. Low prices of power semiconductors and multilevel inverters with high power quality have been recently investigated. However, the conventional multilevel inverter topology is unsuitable for the small-scale renewable distributed generation system, because the number of devices of such topology increases with increasing output voltage level. In this paper, a single-phase multilevel inverter based on H-bridge, with DC_Link divided by bi-directional switches, is proposed. The proposed topology has almost half the number of devices of the conventional multilevel inverter topology when these inverters have the same output voltage level. Double Fourier series solution is mainly used when comparing PWM output harmonic components of various inverter topologies. Harmonic components of the proposed multilevel inverter, which have been analyzed by double Fourier series, are compared with those of the conventional multilevel inverter. An inverter prototype is then developed to verify the validity of the theoretical analysis.

Timoshenko beam model for vibrational analysis of double-walled carbon nanotubes bridged on substrate

  • Jiang, Jingnong;Wang, Lifeng
    • Current Applied Physics
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    • v.17 no.12
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    • pp.1670-1690
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    • 2017
  • This paper proposes a continuum three-segment double Timoshenko beam (TSDTB) model to investigate free vibration of double-walled carbon nanotubes (DWCNTs) bridged on a silicon channel. Accurate explicit formulas of the van der Waals (vdW) interactions between each tube as well as between the tubes and a substrate are derived for a better prediction of the vibrational behaviors of the DWCNTs. An analytical modified Fourier series method (MFSM) is developed for the vibrational analysis of the TSDTB model. Numerical results show the good convergence characteristics and accuracy of the MSFM. The overlapped lengths between DWCNTs and the substrate at both ends have almost no effects on the lower natural frequencies of the TSDTB model when the overlapped lengths are long enough. Moreover, the natural frequencies of the TSDTB model are much less than of those of one-segment double Timoshenko beam (OSDTB) model with clamped supported boundary condition, whereas the TSDTB model can be equivalent to the simply supported OSDTB model under certain condition. In addition, the effects of vdW interaction coefficients on the vibrational behaviors of the DWCNTs are also revealed. The obtained results in this work should be greatly helpful in the design and application of CNTs-based nanomechanical resonators.

The Vibration Analysis of Metal-Piezoceramic Laminated Thin Plates by Using a Equivalent Method (등가화 방법을 이용한 금속;압전 세라믹 적층평판의 진동해석)

  • 고영준;남효덕;장호경
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.13 no.1
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    • pp.39-46
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    • 2000
  • An analysis of the free vibration for the metal-piezoceramic laminated thin plates is described. The purpose of this study is to develop a equivalent method for the free vibration analysis of metal-piezoce-ramic laminated thin plate which are not sysmmetric about the adhered layer and the piezoelectric effect. In order to confirm the validity of the vibration analysis, double Fourier sine series is used as a modal displacement function of a metal-piezoceramic laminated thin plate and applied to the free vibration analysis of the plate under various boundary conditions.

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Calculation of Magnetic Field for Cylindrical Stator Coils in Permanent Magnet Spherical Motor

  • Li, Hongfeng;Ma, Zigang;Han, Bing;Li, Bin;Li, Guidan
    • Journal of Electrical Engineering and Technology
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    • v.13 no.6
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    • pp.2158-2167
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    • 2018
  • This paper analyzed the magnetic field produced by the cylindrical stator coils of permanent magnet spherical motor (PMSM). The elliptic equations about the vector magnetic potential were given. Given that the eddy current effects are neglected, the magnet field of the PMSM is regarded as irrotational field, which can be calculated by scalar magnetic potential. The current density of cylindrical stator coil was proposed based on the definition of current density. The expression of current density of stator coil was obtained according to the double Fourier series decomposition and spherical harmonic functions. Then the magnetic flux density for scalar magnetic potential was derived. Further, the influence of different parameters on radial flux density was also analyzed. Finally, the results by the analytical method in this paper were validated by finite element analysis (FEA).