• Title/Summary/Keyword: analytical solutions

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Torque Analysis of Magnetic Spur Gear with Radial Magnetized Permanent Magnets based on Analytical Method (해석적 방법을 이용한 반경방향 영구자석을 갖는 자기 스퍼 기어의 토크특성해석)

  • Min, Kyoung-Chul;Choi, Jang-Young;Sung, So-Young;Park, Jong-Won
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.64 no.4
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    • pp.545-551
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    • 2015
  • This paper deals with torque analysis of magnetic spur gear with radial magnetized permanent magnets based on analytical method. The analysis is implemented in three parts: First, on the basis of magnetic vector potential and a two-dimensional (2D) polar-coordinate system, the magnetic field solution due to permanent magnet of source gear are obtained. And by using derived magnetic field solutions, the analytical solutions for external magnetic field distribution which affects load gear are obtained. Second, by using coordinate conversion, external magnetic field which is on the primary coordinate system is converted to the secondary coordinate system. Finally, the load gear is reduced to equivalent current densities, and the torque is computed on these currents in the external field of the source magnet. These analytical results are validated by comparing with the 2-D finite element analysis (FEA).

Analytical Solution for Long Waves on Axis-Symmetric Topographies (축 대칭 지형 위를 전파하는 장파의 해석해)

  • Jung, Tae-Hwa;Lee, Changhoon;Cho, Yong-Sik;Lee, Jin-Woo
    • 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.

Analytical solutions using a higher order refined theory for the stability analysis of laminated composite and sandwich plates

  • Kant, T.;Swaminathan, K.
    • Structural Engineering and Mechanics
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    • v.10 no.4
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    • pp.337-357
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    • 2000
  • Analytical formulations and solutions for the first time, to the stability analysis of a simply supported composite and sandwich plates based on a higher order refined theory, developed by the first author and already reported in the literature are presented. The theoretical model presented herein incorporates laminate deformations which account for the effects of transverse shear deformation, transverse normal strain/stress and a nonlinear variation of inplane displacements with respect to the thickness coordinate - thus modelling the warping of transverse cross sections more accurately and eliminating the need for shear correction coefficients. The equations of equilibrium are obtained using the Principle of Minimum Potential Energy (PMPE). The comparison of the results using this higher order refined theory with the available elasticity solutions and the results computed independently using the first order and the other higher order theories developed by other investigators and available in the literature shows that this refined theory predicts the critical buckling load more accurately than all other theories considered in this paper. New results for sandwich laminates are also presented which may serve as a benchmark for future investigations.

Eddy Current Loss Analysis in Radial Flux Type Synchronous Permanent Magnet Coupling using Space Harmonic Methods (공간고조파법을 이용한 반경방향 영구자석을 갖는 자기커플링의 와전류 손실 해석)

  • Min, Kyoung-Chul;Kang, Han-Bit;Park, Min-Gyu;Cho, Han-Wook;Choi, Jang-Young
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.63 no.10
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    • pp.1377-1383
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    • 2014
  • This paper deals with eddy current loss of magnetic coupling with radial permanent magnet (PM) using analytical method such as a space harmonic method. Superposition of two kinds analysis model is used to analyze eddy current loss induced in inner PM and outer PM of magnetic coupling. When the eddy current is induced, the environmental temperature increases, and the permanent magnet(PM) characteristics are degraded because the performance of PM is greatly influenced by temperature rise. Hence, the calculation of eddy current loss becomes an important factor in the magnetic coupling. In order to analyze eddy current loss, first, on the basis of the magnetic vector potential and two-dimensional(2-D) polar-coordinate system, the magnetic field solutions of the radial magnetized PM are obtained. And we obtain the analytical solutions for the eddy current density produced by permanent magnet. Lastly, analytical solutions for eddy current loss are derived by using equivalent, electrical resistance calculated from magnet volume and analytical solution for eddy current density. This analytical results are validated by comparing with the 2-D finite element analysis (FEA).

Analytical Solution for Flow Field by Arbitrarily-Located Multi Injection-Pumping Wells

  • Yoo, In-Wook;Lee, Kang-Kun
    • Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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    • 2001.09a
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    • pp.79-82
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    • 2001
  • Analytical solutions have been derived to delineate the capture zone created by pumping wells for the remediation design of contaminated groundwater. These previous analytical solutions are often restricted to pumping wells only, specific well locations, a limited number of wells, and an isotropic aquifer. Analytical solution was developed to deal with arbitrarily located multi injection-pumping wells in an anisotropic homogeneous aquifer. The solution presented in this study provides a simple, easy method for determining tile complex flow field caused by multi injection-pumping wells at different rates, and will consequently be useful in pump-and-treat design.

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Analytical Design of the Space Debris Collision Avoidance Maneuver based on Relative Dynamics (상대운동방정식 기반의 우주파편 충돌회피기동의 해석적 설계기법)

  • Cho, Dong-Hyun;Kim, Hae-Dong;Lee, Sang-Cherl
    • Journal of Institute of Control, Robotics and Systems
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    • v.19 no.11
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    • pp.1048-1052
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    • 2013
  • Recently, many countries have attempted to protect their satellites from damage caused by space debris. To design these collision avoidance maneuvers, optimal algorithms based on numerical simulations are widely used due to their practicality. However, these algorithms often require a great expenditure of time in order to find solutions. Therefore, in this paper, a simple analytical strategy is suggested to find the initial prediction required to find these numerical solutions for collision avoidance maneuvers by using relative dynamics for the rendezvous and docking problems. For this analytical strategy, the simple dynamics on the CW (Clohessy-Wiltshire) frame is adopted as an attempt to introduce an analytical solution.

Vibration control of laminated composite plates using embedded smart layers

  • Reddy, J.N.;Krishnan, S.
    • Structural Engineering and Mechanics
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    • v.12 no.2
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    • pp.135-156
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    • 2001
  • Analytical solutions and finite element results of laminated composite plates with smart material layers embedded in them are presented in this study. The third-order plate theory of Reddy is used to study vibration suppression characteristics. The analytical solution for simply supported boundary conditions is based on the Navier solution procedure. The velocity feedback control is used. Parametric effects of the position of the smart material layers, material properties, and control parameters on the suppression time are investigated. It has been found that (a) the minimum vibration suppression time is achieved by placing the smart material layers farthest from the neutral axis, (b) using thinner smart material layers have better vibration attenuation characteristics, and, (c) the vibration suppression time is larger for a lower value of the feedback control coefficient.

Free Vibration of a Thin Plate with Small Deflections by Semi-Analytical Approach (반해석적 방법에 의한 작은 변위를 가지는 얇은판의 자유진동해석)

  • 최덕기
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.8
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    • pp.1967-1973
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    • 1994
  • The free vibration of a thin plate with three different boundary conditions is discussed in this paper. A semi-analytical approach to the plate problems has been exploited using computer algebra system(CAS). The approximate solutions are assumed as algebraic polynomials that satisfy the appropriate boundary conditions. In order to solve problems, Galerkin method is used, which is known as an ineffective tool for practical engineering problems, being involved with a large number of multiple integration and differentiation. All the admissible functions used in this paper are generated automatically by CAS otherwise a tedious algebraic manipulations should be done by hand. One, six and fifteen-term solutions in terms of frequency parameters are presented and compared with exact solutions. Even using one-term solution, the comparison with existing data shows good agreement and accuracy of the present method.

Analysis of Orthotropic Spherical Shells under Symmetric Load Using Runge-Kutta Method (Runge-Kutta법을 이용한 축대칭 하중을 받는 직교 이방성 구형쉘의 해석)

  • Kim, Woo-Sik;Kwun, Ik-No;Kwun, Taek-Jin
    • Journal of Korean Association for Spatial Structures
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    • v.2 no.3 s.5
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    • pp.115-122
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    • 2002
  • It is often hard to obtain analytical solutions of boundary value problems of shells. Introducing some approximations into the governing equations may allow us to get analytical solutions of boundary value problems. Instead of an analytical procedure, we can apply a numerical method to the governing equations. Since the governing equations of shells of revolution under symmetric load are expressed by ordinary differential equations, a numerical solution of ordinary differential equations is applicable to solve the equations. In this paper, the governing equations of orthotropic spherical shells under symmetric load are derived from the classical theory based on differential geometry, and the analysis is numerically carried out by computer program of Runge-Kutta methods. The numerical results are compared to the solutions of a commercial analysis program, SAP2000, and show good agreement.

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Analytical solutions for bending of transversely or axially FG nonlocal beams

  • Nguyen, Ngoc-Tuan;Kim, Nam-Il;Lee, Jaehong
    • Steel and Composite Structures
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    • v.17 no.5
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    • pp.641-665
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    • 2014
  • This paper presents the analytical solutions for the size-dependent static analysis of the functionally graded (FG) beams with various boundary conditions based on the nonlocal continuum model. The nonlocal behavior is described by the differential constitutive model of Eringen, which enables to this model to become effective in the analysis and design of nanostructures. The elastic modulus of beam is assumed to vary through the thickness or longitudinal directions according to the power law. The governing equations are derived by using the nonlocal continuum theory incorporated with Euler-Bernoulli beam theory. The explicit solutions are derived for the static behavior of the transversely or axially FG beams with various boundary conditions. The verification of the model is obtained by comparing the current results with previously published works and a good agreement is observed. Numerical results are presented to show the significance of the nonlocal effect, the material distribution profile, the boundary conditions, and the length of beams on the bending behavior of nonlocal FG beams.