• Title/Summary/Keyword: elliptic functions

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AERODYNAMIC OPTIMIZATION OF SUPERSONIC WING-NACELLE CONFIGURATION USING AN UNSTRUCTURED ADJOINT METHOD

  • Kim Hyoung-Jin;Obayashi Shigeru;Nakahashi Kazuhiro
    • 한국전산유체공학회:학술대회논문집
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    • 2000.05a
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    • pp.60-65
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    • 2000
  • An aerodynamic design method has been developed by using a three-dimensional unstructured Euler code and an adjoint code with a discrete approach. The resulting adjoint code is applied to a wing design problem of super-sonic transport with a wing-body-nacelle configuration. Hicks-Henne shape functions are adopted far the surface geometry perturbation, and the elliptic equation method is employed fer the interior grid modification during the design process. Interior grid sensitivities are neglected except those for design parameters associated with nacelle translation. The Sequential Quadratic Programming method is used to minimize the drag with constraints on the lift and airfoil thickness. Successful design results confirm validity and efficiency of the present design method.

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Nonlinear forced vibrations of multi-scale epoxy/CNT/fiberglass truncated conical shells and annular plates via 3D Mori-Tanaka scheme

  • Mirjavadi, Seyed Sajad;Forsat, Masoud;Barati, Mohammad Reza;Hamouda, AMS
    • Steel and Composite Structures
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    • v.35 no.6
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    • pp.765-777
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    • 2020
  • In the context of classic conical shell formulation, nonlinear forced vibration analysis of truncated conical shells and annular plates made of multi-scale epoxy/CNT/fiberglass composites has been presented. The composite material is reinforced by carbon nanotube (CNT) and also fiberglass for which the material properties are defined according to a 3D Mori-Tanaka micromechanical scheme. By utilizing the Jacobi elliptic functions, the frequency-deflection curves of truncated conical shells and annular plates related to their forced vibrations have been derived. The main focus is to study the influences of CNT amount, fiberglass volume, open angle, fiber angle, truncated distance and force magnitude on forced vibrational behaviors of multi-scale truncated conical shells and annular plates.

CONVOLUTION SUMS AND THEIR RELATIONS TO EISENSTEIN SERIES

  • Kim, Daeyeoul;Kim, Aeran;Sankaranarayanan, Ayyadurai
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.4
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    • pp.1389-1413
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    • 2013
  • In this paper, we consider several convolution sums, namely, $\mathcal{A}_i(m,n;N)$ ($i=1,2,3,4$), $\mathcal{B}_j(m,n;N)$ ($j=1,2,3$), and $\mathcal{C}_k(m,n;N)$ ($k=1,2,3,{\cdots},12$), and establish certain identities involving their finite products. Then we extend these types of product convolution identities to products involving Faulhaber sums. As an application, an identity involving the Weierstrass ${\wp}$-function, its derivative and certain linear combination of Eisenstein series is established.

Free vibrations of inclined arches using finite elements

  • Chucheepsakul, Somchai;Saetiew, Wasuroot
    • Structural Engineering and Mechanics
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    • v.13 no.6
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    • pp.713-730
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    • 2002
  • This paper presents a finite element approach for determining the natural frequencies for planar inclined arches of various shapes vibrating in three-dimensional space. The profile of inclined arches, represented by undeformed centriodal axis of cross-section, is defined by the equation of plane curves expressed in the rectangular coordinates which are : circular, parabolic, sine, elliptic, and catenary shapes. In free vibration state, the arch is slightly displaced from its undeformed position. The linear relationship between curvature-torsion and axial strain is expressed in terms of the displacements in three-dimensional space. The finite element discretization along the span length is used rather than the total are length. Numerical results for arches of various shapes are given and they are in good agreement with those reported in literature. The natural frequency parameters and mode shapes are reported as functions of two nondimensional parameters: the span to cord length ratio (e) and the rise to cord length ratio (f).

Grid Generation about Full Aircraft Configuration Using Interactive Grid Generator (상호 대화형 격자생성 환경을 이용한 항공기 전기체 격자계 생성)

  • Kim Y. S.;Kwon J. H.
    • 한국전산유체공학회:학술대회논문집
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    • 1999.11a
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    • pp.145-151
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    • 1999
  • An Interactive grid generation program(KGRID) with graphical user interface(GUI) has been improved. KGRID works on the UNLX environment and GUI has been implemented with OSF/Motif and X Toolkit and the graphics language is Open GL for visualization of the 3D objects. It supports more convenient user environment to generate 2D and 3D multi-block structured grid systems. It provides various useful field grid generation methods, which are the algebraic methods, the elliptic partial differential equations method and the predictor-corrector method. It also supports 3D surface grid generation with NURBS(Non-Uniform Rational B-Spline) and various stretching functions to control grid points distribution on curves and surfaces. And some menus are added to perform flexible management, for the objects. We generated surface and field grid system about full aircraft configuration using KGRID. The performance and stability of the KGRID is verified through the generation of the grid system about a complex shape.

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Eigenvalue Analysis of a Membrane Using the Multiscale Adaptive Wavelet-Galerkin Method (멀티스케일 적응 웨이블렛-갤러킨 기법을 이용한 박막 고유치 문제 해석)

  • Yi, Yong-Sub;Kim, Yoon-Young
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.28 no.3
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    • pp.251-258
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    • 2004
  • Since the multiscale wavelet-based numerical methods allow effective adaptive analysis, they have become new analysis tools. However, the main applications of these methods have been mainly on elliptic problems, they are rarely used for eigenvalue analysis. The objective of this paper is to develop a new multiscale wavelet-based adaptive Galerkin method for eigenvalue analysis. To this end, we employ the hat interpolation wavelets as the basis functions of the finite-dimensional trial function space and formulate a multiresolution analysis approach using the multiscale wavelet-Galerkin method. It is then shown that this multiresolution formulation makes iterative eigensolvers very efficient. The intrinsic difference-checking nature of wavelets is shown to play a critical role in the adaptive analysis. The effectiveness of the present approach will be examined in terms of the total numbers of required nodes and CPU times.

Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam

  • Selmi, Abdellatif
    • Smart Structures and Systems
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    • v.26 no.3
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    • pp.361-371
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    • 2020
  • Exact solution for nonlinear behavior of clamped-clamped functionally graded (FG) buckled beams is presented. The effective material properties are considered to vary along the thickness direction according to exponential-law form. The in-plane inertia and damping are neglected, and hence the governing equations are reduced to a single nonlinear fourth-order partial-integral-differential equation. The von Kármán geometric nonlinearity has been considered in the formulation. Galerkin procedure is used to obtain a second order nonlinear ordinary equation with quadratic and cubic nonlinear terms. Based on the mode of the corresponding linear problem, which readily satisfy the boundary conditions, the frequencies for the nonlinear problem are obtained using the Jacobi elliptic functions. The effects of various parameters such as the Young's modulus ratio, the beam slenderness ratio, the vibration amplitude and the magnitude of axial load on the nonlinear behavior are examined.

SCHEDULING TECHNIQUE FOR CONTROL STEP (스케듈링 기법 연구)

  • JeongYoungSong;NamWooBack
    • Journal of the Korean Geophysical Society
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    • v.4 no.3
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    • pp.163-173
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    • 2001
  • This paper deals with scheduling problems which are the most important subtask in High-Level Synthesis. Especially, we have concentrated our attentions on the data-path scheduling which can get the structural informaion trom the behavioral algorithm as a first step in synthesis procedure. Suggest Forward scheduling methode is executed the ASAP and ALAP scheduling to use the fifth - order elliptic wave filter of a standard benchmark moedl, and then it is drawing up T.N matrix table by the number resource and control-step, using the table extract of the simple than down-limit value of the control-step for the number of given resource th use this table. All of existing list scheduling techniques determine the priority function first, and then do the operation scheduling, But, the suggested forward scheduling technique does the schedule first, and determines the priority functions if needed in scheduling process.

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Free Vibration Analysis of Stepped Noncircular Arches with Shear Deformation (전단변형을 고려한 불연속 단면을 갖는 변화곡률 아치의 자유진동 해석)

  • Oh, Sang-Jin;Mo, Jeong-Man;Jin, Tae-Ki
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.11a
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    • pp.768-771
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    • 2005
  • The purpose of this paper is to investigate the free vibration of stepped noncircular arches. Taking into account the effects of axial deformation, rotatory inertia and shear deformation, the governing differential equations are solved numerically for the elliptic and sinusoidal geometries with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. The lowest four natural frequencies are presented as functions of four non-dimensional system parameters: the arch rise to span length ratio, the slenderness ratio, the section ratio, and the discontinuous sector ratio.

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A Filter Synthesis Method for Multi-Band Filter Design (다중 대역 필터 설계를 위한 필터 합성법)

  • Lee, Hye-Sun;Lee, Ja-Hyeon;Lim, Yeong-Seog
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.21 no.11
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    • pp.1259-1268
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    • 2010
  • In this paper, we presented a new LC prototype synthesis method for the multi-band filter. For synthesis a multi-band filter with the required frequency response, we proposed the diagram of poles and zeros, also, we proposed the optimization process for finding the combination of optimized poles and zeros. From the transfer and reflection functions calculated from poles and zeros, we performed the quasi-elliptic LC prototype synthesis of multi-band filter. Using the proposed LC prototype synthesis method of multi-band filter, dual-band filter operating at GSM(880~960 MHz) and ISM(2,400~2,500 MHz) and triple-band filter operating at GSM(880~960 MHz) and ISM(2,400~2,500, 5,725~5,850 MHz) were designed and fabricated.