• Structural Engineering and Mechanics
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• v.23 no.5
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• pp.525-542
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• 2006

On the basis of equilibrium equations for static electric and magnetic fields, two unknown functions related to electric and magnetic fields were firstly introduced to rewrite the governing equations, boundary conditions and initial conditions for mechanical field. Then by introducing a dependent variable and a special function satisfying the inhomogeneous mechanical boundary conditions, the governing equation for a new variable with homogeneous mechanical boundary conditions is obtained. By using the separation of variables technique as well as the electric and magnetic boundary conditions, the dynamic problem of a functionally graded magneto-electro-elastic hollow sphere under spherically symmetric deformation is transformed to two Volterra integral equations of the second kind about two unknown functions of time. Cubic Hermite polynomials are adopted to approximate the two undetermined functions at each time subinterval and the recursive formula for solving the integral equations is derived. Transient responses of displacements, stresses, electric and magnetic potentials are completely determined at the end. Numerical results are presented and discussed.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.39-49
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• 2010

This paper deals with the second-order differential equation (p(t)x'(t))' + g(t)f(t, x(t), x'(t)) = 0, a.e. in (0, $\infty$) with the boundary conditions $$x(0)={\int}^{\infty}_0g(s)x(s)ds,\;{lim}\limits_{t{\rightarrow}{\infty}}p(t)x'(t)=0,$$ where $g\;{\in}\;L^1[0,{\infty})$ with g(t) > 0 on [0, $\infty$) and ${\int}^{\infty}_0g(s)ds\;=\;1$, f is a g-Carath$\acute{e}$odory function. By applying the coincidence degree theory, the existence of at least one solution is obtained.

• Journal of Electrical Engineering and Technology
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• v.4 no.2
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• pp.240-248
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• 2009

An approach to control the position for an interior permanent magnet synchronous motor (IPMSM) based on an adaptive integral binary observer is described. The binary controller with a binary observer is composed of a main loop regulator and an auxiliary loop regulator. One of its key features is that it alleviates chatter in the constant boundary layer. However, steady state estimation accuracy and robustness are dependent upon the thickness of the constant boundary layer. In order to improve the steady state performance of the binary observer and eliminate the chattering problem of the constant boundary layer, a new binary observer is formed by adding extra integral dynamics to the existing switching hyperplane equation. Also, the proposed adaptive integral binary observer applies an adaptive scheme because the parameters of the dynamic equations such as the machine inertia and the viscosity friction coefficient are not well known. Furthermore, these values can typically be easily changed during normal operation. However, the proposed observer can overcome the problems caused by using the dynamic equations, and the rotor position estimation is constructed by integrating the rotor speed estimated with a Lyapunov function. Experimental results obtained using the proposed algorithm are presented to demonstrate the effectiveness of the approach.

• Structural Engineering and Mechanics
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• v.71 no.6
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• pp.627-641
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• 2019

The paper focuses on bending analysis of the functionally graded (FG) plates with arbitrary shapes and boundary conditions. The material property of FG plates is modelled by using the power law distribution. Based on the first order shear deformation plate theory (FSDT), the governing equations as well as boundary conditions are formulated and obtained by using the principle of virtual work. The coupled Boundary Element-Radial Basis Function (BE-RBF) method is established to solve the complex FG plates. The proposed methodology is developed by applying the concept of the analog equation method (AEM). According to the AEM, the original governing differential equations are replaced by three Poisson equations with fictitious sources under the same boundary conditions. Then, the fictitious sources are established by the application of a technique based on the boundary element method and approximated by using the radial basis functions. The solution of the actual problem is attained from the known integral representations of the potential problem. Therefore, the kernels of the boundary integral equations are conveniently evaluated and readily determined, so that the complex FG plates can be easily computed. The reliability of the proposed method is evaluated by comparing the present results with those from analytical solutions. The effects of the power index, the length to thickness ratio and the modulus ratio on the bending responses are investigated. Finally, many interesting features and results obtained from the analysis of the FG plates with arbitrary shapes and boundary conditions are demonstrated.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.329-341
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• 2018

This paper considers the smooth receding contact problem between a homogeneous half-plane and a composite laminate composed of an inhomogeneously coated elastic layer. The inhomogeneity of the elastic modulus of the coating is approximated by an exponential function along the thickness dimension. The three-component structure is pressed together by either a concentrated force or uniform pressures applied at the top surface of the composite laminate. Both semianalytical and finite element analysis are performed to solve for the extent of contact and the contact pressure. In the semianalytical formulation, Fourier integral transformation of governing equations and boundary conditions leads to a singular integral equation of Cauchy-type, which can be numerically integrated by Gauss-Chebyshev quadrature to a desired degree of accuracy. In the finite element modeling, the functionally graded coating is divided into homogeneous sublayers and the shear modulus of each sublayer is assigned at its lower boundary following the predefined exponential variation. In postprocessing, the stresses of any node belonging to sublayer interfaces are averaged over its surrounding elements. The results obtained from the semianalytical analysis are successfully validated against literature results and those of the finite element modeling. Extensive parametric studies suggest the practicability of optimizing the receding contact peak stress and the extent of contact in multilayered structures by the introduction of functionally graded coatings.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.3
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• pp.258-268
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• 2008

The radiation potential of a ship advancing in waves is studied using the 3D time-domain forward-speed free-surface Green function and the Green integral equation. Numerical solutions are obtained by making use of the 2nd order BEM(Boundary Element Method) which make it possible to take account of the line integral along the waterline in a rigorous manner. The 6 degree of freedom motion memory functions of a hemisphere and the Wigley seakeeping model obtained by direct integration of the time-domain 3D potentials over the wetted surface are presented for various Froude numbers.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.1
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• pp.71-80
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• 2007

A control approach for the sensorless speed control of interior permanent magnet synchronous motor(IPMSM) based on adaptive integral the binary is proposed. With a main loop regulator and an auxiliary loop regulator, the binary observer has a property of the chattering alleviation in the constant boundary layer. However, the width of the constant boundary limits the steady state estimation accuracy and robustness. In order to improve the steady state performance of the binary observer, the binary observer is formed by adding extra integral augmented switching the hyperplane equation. By mean of integral characteristics, the rotor speed can be finely estimated and utilized for a sensorless speed controller for IPMSM. The proposed adaptive integral binary observer applies an adaptive scheme, because the parameters of the dynamic equations such as the machine inertia or the viscosity friction coefficient is not well known and these values can be easily changed generally during normal operation. Therefore, the observer can overcome the problem caused by using the dynamic equations, and the rotor speed estimation is constructed by using the Lyapunov function. The experimental results of the proposed algorithm are presented to demonstrate the effectiveness of the approach.

• Proceedings of the KIEE Conference
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• 2006.04b
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• pp.229-231
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• 2006

The paper presents a sensorless speed control of interior permanent magnet synchronous motors using an adaptive integral binary observer in view of composition with a main loop regulator and an auxiliary loop regulator. The binary observer has a property of the chattering alleviation in the constant boundary layer; however, the steady state estimation accuracy and robustness are dependent upon with width of the constant boundary. In order to improve the steady state performance of the binary observer, the binary observer is formed by adding extra integral dynamic to the switching hyperplane equation.

• Journal of Mechanical Science and Technology
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• v.18 no.9
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• pp.1549-1558
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• 2004

This study is concerned with the general solution of the field intensity factors and energy release rate for a Griffith crack in a piezoelectric ceramic of finite radius under combined anti-plane mechanical and in-plane electrical loading. Both electrically continuous and impermeable crack surface conditions are considered. Employing Mellin transforms and Fourier series, the problem is reduced to dual integral forms. The solution to the resulting expressions is expressed in terms of Fredholm integral equation of the second kind. The solutions are provided to study the influence of the crack length, the crack surface boundary conditions on the intensity factors and the energy release rate.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.10
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• pp.89-101
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• 1995

선형 탄성 등방성 물체 내에 있는 일반적인 복합모드 크랙 문제들을 해석하기 위한 이중 경계적분방정식의 일반식과 계산해법이 제시되었다. 크랙면이 포함된 물체 해석에 있어서 유일한 해를 얻기 위하여, 한 면상의 점에는 변위 경계적분방정식이 적용되었고 마주하고 있는 상대면 상의 점에는 인력 경계적분방정식이 적용되었다. 인력 및 변위 경계적분방정식의 강특이해 및 초특이해 적분항들은 수치해법을 적용하기 전에 정상화되었다. 정상화과정 중 보정되는 강특이적분항이 상대 크랙면 상의 특이해 요소를 따라 직접 적분되는 것을 격리시키기 위하여, 특이해 적분 경로를 완만한 곡면으로 우회시킨 가상의 비특이해 보조경계로 대치하여 적분값을 계산하였다. 제시된 해법의 정확성과 효율성을 예시하기 위하여, 2차원 및 3차원 크랙 문제의 변형 후 모습과 응력강도계수 계산 결과를 보였다.