• Structural Engineering and Mechanics
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• 제38권6호
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• pp.753-765
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• 2011

The radial vibration behaviors of a circular cylindrical composite piezoelectric transducer (CPT) are investigated. The CPT is composed of a piezoelectric ring polarized in the radial direction and an elastic ring graded in power-law variation form along the radial direction. The governing equations for plane stress state problem under the harmonic excitation are derived and the exact solutions for both piezoelectric and functionally graded elastic rings are obtained. The characteristic equations for resonant and anti-resonant frequencies are established. The presented methodology is fit to carry out the parametric investigation for composite piezoelectric transducers (CPTs) with arbitrary thickness in radial direction. With the aid of numerical analysis, the relationship between the radial vibration behaviors of the cylindrical CPT and the material inhomogeneity index of the functionally graded elastic ring as well as the geometric parameters of the CPTs are illustrated and some important features are reported.

• 대한전기학회논문지:전기기기및에너지변환시스템부문B
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• 제54권12호
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• pp.576-585
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• 2005

This paper deals with the electromagnetic field analysis of slotless brushless permanent magnet machines with three different magnetization patterns such as Halbach, parallel and radial magnetization. The magnetization modeling of Halbach, parallel and radial magnetization is performed analytically. And then, analytical solutions for open-circuit field distributions, armature reaction field distributions, flux linkages due to PMs and stator windings, torque, back-emf and inductance are derived in terms of magnetic vector potential and two-dimensional (2-d) polar coordinate systems. The analytical results are validated extensively by finite element (FE) analyses. The magnet volume required in order to produce identical flux density is compared with each magnetization. Finally, analytical solutions and derivation procedures of those presented in this paper can be applied to slotless and slotted brushless permanent magnet AC and DC machines.

• 대한설비공학회지:설비저널
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• 제11권3호
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• pp.9-17
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• 1982

In this paper, temperature distributions in radial fin of hyperbolic profile for steady -state with no heat generation are obtained by one-dimensional analytical method, finite difference method and experiment respectively. Heat flow rate and fin efficiency from the fin model are obtained by analytical method. To compare the exact solutions obtained by theoretical analysis with the results obtained by finite difference method, cylindrical shape is selected. Particularly, equations of finite difference method for cylindrical shape with irregular boundary are rearranged and formulated. Consequently, temperature distributions in radial fin can certify that are similar to exact solutions. From theoretical analysis, the effects according to heat flow rate and fin efficiency are related to variation of parameters which are fin thickness ${\delta}_o$, fin base temperature $T_o$, thermal conductivity K with same basic dimensions and the fleets are studied and compared.

• Geomechanics and Engineering
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• 제16권6호
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• pp.609-618
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• 2018

A new mechanical model for predicting the vibration of a pipe pile embedded in longitudinally layered visco-elastic media with radial inhomogeneity is proposed by extending Novak's plain-strain model and complex stiffness method to consider viscous-type damping. The analytical solutions for the dynamic impedance, the velocity admittance and the reflected signal of wave velocity at the pile head are also derived and subsequently verified by comparison with existing solutions. An extensive parametric analysis is further performed to examine the effects of shear modulus, viscous damping coefficient, coefficient of disturbance degree, weakening or strengthening range of surrounding soil and longitudinal soft or hard interbedded layer on the velocity admittance and the reflected signal of wave velocity at the pile head. It is demonstrated that the proposed model and the obtained solutions provide extensive possibilities for practical application compared with previous related studies.

• 한국소음진동공학회논문집
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• 제15권4호
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• pp.412-420
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• 2005

This article proposes analytical solutions for sound radiation from radial vibration modes of a thick annular disk. Structural eigensolutions are calculated using the transfer matrix method. The far-field sound pressure distribution is obtained using two alternate methods. In the first method, pressure is calculated using the Rayleigh integral technique. The second method treats sound radiating radial surfaces as cylindrical radiators of finite length. The Sinc function approach is employed for calculations. Acoustic powers and radiation efficiencies of radial modes are also determined from the far-field sound pressure calculations. Analytical predictions match well with measured data as well as computational results from a finite element code in terms of structural eigensolutions and from a boundary element code in terms of sound pressure, directivity etc.

• Geomechanics and Engineering
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• 제13권4호
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• pp.585-600
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• 2017

This study deals with simple solutions for a spherical or circular opening excavated in elastic-brittle plastic rock mass compatible with a linear Mohr-Coulomb (M-C) or a nonlinear Hoek-Brown (H-B) yield criterion. Based on total strain approach, the closed-form solutions of stresses and displacement are derived simultaneously for circular and spherical openings using original H-B and M-C yield criteria. Two simple numerical procedures are proposed for the solution of generalized H-B and M-C yield criteria. Based on incremental approach, the similarity solution is derived for circular and spherical openings using generalized H-B and M-C yield criteria. The classical Runge-Kutta method is used to integrate the first-order ordinary differential equations. Using three data sets for M-C and H-B models, the results of the radial displacements, the spreading of the plastic radius with decreasing pressure, and the radial and circumferential stresses in the plastic region are compared. Excellent agreement among the solutions is obtained for all cases of spherical and circular openings. The importance of the use of proper initial values in the similarity solution is discussed.

• 전기학회논문지
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• 제63권10호
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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).

• 대한수학회보
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• 제50권3호
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• pp.839-865
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• 2013

We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system $$\large(S) \hfill{400} \{\array{-{\varepsilon}^2{\Delta}u+V_1(x)u=K(x)Q_u(u,v)\;in\;\mathbb{R}^N,\\-{\varepsilon}^2{\Delta}v+V_2(x)v=K(x)Q_v(u,v)\;in\;\mathbb{R}^N,\\u,v{\in}W^{1,2}(\mathbb{R}^N),\;u,v&gt;0\;in\;\mathbb{R}^N,}$$ where ${\varepsilon}$ is a small positive parameter; $V_1$, $V_2{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ and $K{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ are radially symmetric potentials; Q is a $(p+1)$-homogeneous function and p is subcritical, that is, 1 < $p$ < $2^*-1$, where $2^*=2N/(N-2)$ is the critical Sobolev exponent for $N{\geq}3$.

• 대한기계학회논문집B
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• 제23권2호
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• pp.243-253
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• 1999

The dual reciprocity boundary element method (DRBEM) is used to solve the Graetz problem of laminar flow inside circular duct. In this method the domain integral tenn of boundary integral equation resulting from source term of governing equation is transformed into equivalent boundary-only integrals by using the radial basis interpolation function, and therefore complicate domain discretization procedure Is completely removed. Velocity profile is obtained by solving the momentum equation first and then, using this velocities as Input data, energy equation Is solved to get the temperature profile by advancing from duct entrance through the axial direction marching scheme. DRBEM solution is tested for the uniform temperature and heat flux boundary condition cases. Local Nusselt number, mixed mean temperature and temperature profile inside duct at each dimensionless axial location are obtained and compared with exact solutions for the accuracy test Solutions arc in good agreement at the entry region as well as fully developed region of circular duct, and their accuracy are verified from error analysis.

• 한국소음진동공학회논문집
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• 제19권11호
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• pp.1133-1143
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• 2009

좁은 슬롯을 포함한 디스크 브레이크 로터의 소음 방사특성을 전산해석과 이론적 계산을 합성한 방법으로 검토하였다. 첫 단계로 로터와 기본 치수가 동일하고 동일한 슬롯을 보유한 후판 환형 디스크의 소음방사 특성을 유한요소해석을 구한 모달 진동 데이터를 바탕으로 기존의 해법을 이용하여 계산하고 수치해석결과로 검증하였다. 다음으로 이 결과를 유한요소해석으로 구한 샘플 로터의 고유진동 특성에 적용, 고유진동으로 인한 소음방사를 계산한 다음 그 결과를 경계요소법을 이용하여 검증하였다. 마지막으로 이 결과를 바탕으로 로터에 고정된 조화가진 및 로터 주위를 회전하는 조화력에 의해 방사되는 소음 및 진동 특성을 검토하였다.