• Journal of the Korean Institute of Telematics and Electronics
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• v.10 no.1
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• pp.1-8
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• 1973

It is often difficult, or almost impossible, in most cases to obtain the optimal solution to the non-linear control systems by analytical method. In this paper, the authors have treated with the technique of parameteric adaptation which is introduced into the performance index, in order to circumvent the difficulties arising in seal.ch of optimal policy for the non-linear feedback control systems. This approach is shown to provide the advantage of making it possible to design the non-linear feedback control system even if the design specifications are not completely discribed in mathematical form. This is fundamentally due to a certain degree of freedoln in design, which this method allows the designer in establishing the performance index. The effectiveness and feasibilities of this concept are demonstrated by working out some illustrative examples with the performance index of integral quadratic form.

• Coupled systems mechanics
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• v.11 no.3
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• pp.217-231
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• 2022

The present paper is concerned with a delamination analysis of a multilayered frame structure that exhibits non-linear creep behavior. A solution to the strain energy release rate is obtained by considering the time-dependent complementary strain energy in the frame. The mechanical behavior of the frame is treated by using a non-linear stress-strain-time relationship. The time-dependent solution to the strain energy release rate obtained in the present paper holds for a multilayered frame made of arbitrary number of adhesively bonded layers of different thicknesses and material properties. Besides, the dealamination is located arbitrary along the thickness. The solution to the strain energy release rate is verifiedby applying the J-integral approach. A parametric study of the strain energy release rate is carried-out. Two three-layered frame configurations are analyzed in order to evaluate the influence of the delamination crack location along the thickness on the strain energy release rate. The strain energy release is analyzed also for the case when a notch is cut-out in the inner delamination crack arm. The results obtained are compared with these for a frame without a notch.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.159.2-159
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• 2001

The new approach of homogeneous robust control systems synthesis, both linear, and nonlinear and non-stationary is offered. The control is carried out, providing the given phase constrains varied in acceptable limits, in view of constrains on its value and incompleteness of the information about functioning disturbances. The approach is based on introduction of auxiliary integral surfaces, on which the initial moving is projected. As a result the reduced equivalent moving is forming, described by the scalar equation which in many important cases can be integrated directly. On the basis of the obtained equation solving of a synthesis task is carried out and can be reduced to algebraic or integral inequalities. The final relations defined for linear equivalent moving are presented.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2006.06a
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• pp.305-306
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• 2006

Developed in this study is a nonlinear Ekman pumping model to be used in simulating the rotating flows with quasi-three-dimensional Navier-Stokes equations. In this model, the Ekman pumping velocity is given from the solution of the Ekman boundary-layer equations for the region adjacent to the bottom wall of the flow domain; the boundary-layer equations are solved in the momentum-integral form. The developed model is then applied to rotating flows in a rectangular container receiving a time-periodic forcing. By comparing our results with the DNS and experimental data we have validated the developed model. We also compared our results with those given from the classical Ekman pumping model. It was found that our model can predict tile rotating flows more precisely than the classical linear model.

• Journal of Mechanical Science and Technology
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• v.15 no.9
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• pp.1281-1291
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• 2001

The hereditary integral form of a quasi-linear viscoelastic law has been employed. Four new concepts have been employed: 1. a reduced relaxation function with a non-linear exponential function of time, 2. an inverse method to determine the scale factor of the elastic response, 3. an instant elastic recovery strain during unloading, and 4. the results of a constitutive model for cyclic tests may be a function of the Heavyside class. These concepts have been supported by agreement between measured and predicted responses of soft connective tissue to three types of multiple cyclic tests which include rest periods of no extension and alternations between different strain levels. Such agreement has not been attained in the previous studies. Chun and Hubbard (2001) is our companion experimental analysis paper.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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• pp.949-956
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• 2006

The method of Greenwood and Williamson is extended to obtain a solution to the coupled non-linear problem of steady-state electrical and thermal conduction across a crack in a conductive layer, for which the electrical resistivity and thermal conductivity are functions of temperature. The problem can be decomposed into the solution of a pair of non-linear algebraic equations involving boundary values and material properties. The new mixed-boundary value problem given from the thermal and electrical boundary conditions for the crack in the conductive layer is reduced in order to solve a singular integral equation of the first kind, the solution of which can be expressed in terms of the product of a series of the Chebyshev polynomials and their weight function. The non-existence of the solution for an infinite conductor in electrical and thermal conduction is shown. Numerical results are given showing the temperature field around the crack.

• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.655-674
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• 2015

In this paper, a new and simplified method is presented in which the natural frequencies of the uniform and non-uniform beams are calculated through simple mathematical relationships. The various vibration problems such as: Rayleigh beam under variable axial force, axial vibration of a bar with and without end discrete spring, torsional vibration of a bar with an attached mass moment of inertia, flexural vibration of the beam with laterally distributed elastic springs and also flexural vibration of the beam with effects of viscose damping are investigated. The governing differential equations are first obtained and then; according to a harmonic vibration, are converted into single variable equations in terms of location. Through repetitive integrations, the governing equations are converted into weak form integral equations. The mode shape functions of the vibration are approximated using a power series. Substitution of the power series into the integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of a non-trivial solution for system of equations. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained with those obtained from other published references and results of available finite element software.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.916-919
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• 2004

The monopole theory has long been used to model air-pumped effect from the elastic cavities in car tire. This approach models the change of an air as a piston moving backward and forward on a spring and equates local air movements exactly with the volume changes of the system. Thus, the monopole theory has a restricted domain of applicability due to the usual assumption of a small amplitude acoustic wave equation and acoustic monopole theory. This paper describes an approach to predict the air-pumping noise of a car ave with CFD/Kirchhoff integral method. The type groove is simply modeled as piston-cavity-sliding door geometry and with the aid of CFD technique flow properties in the groove of rolling car tyre are acquired. And these unsteady flow data are used as a air-pumping source in the next Cm calculation of full tyre-road geometry. Acoustic far field is predicted from Kirchhoff integral method by using unsteady flow data in space and time, which is provided by the CFD calculation of full tyre-road domain. This approach can cover the non-linearity of acoustic monopole theory with the aid of using Non-linear governing equation in CFD calculation. The method proposed in this paper is applied to the prediction of air-pumping noise of modeled car tyre and the predicted results are qualitatively compared with the experimental data.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.409-445
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• 2016

The class $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ defined in the domain ${\mid}z{\mid}$ < 1 satisfying $Re\;e^{i{\phi}}\((1-{\alpha}+2{\gamma})(f/z)^{\delta}+\({\alpha}-3{\gamma}+{\gamma}\[1-1/{\delta})(zf^{\prime}/f)+1/{\delta}\(1+zf^{\prime\prime}/f^{\prime}\)\]\)(f/z)^{\delta}(zf^{\prime}/f)-{\beta}\)$ > 0, with the conditions ${\alpha}{\geq}0$, ${\beta}$ < 1, ${\gamma}{\geq}0$, ${\delta}$ > 0 and ${\phi}{\in}{\mathbb{R}}$ generalizes a particular case of the largest subclass of univalent functions, namely the class of $Bazilevi{\check{c}}$ functions. Moreover, for 0 < ${\delta}{\leq}{\frac{1}{(1-{\zeta})}}$, $0{\leq}{\zeta}$ < 1, the class $C_{\delta}({\zeta})$ be the subclass of normalized analytic functions such that $Re(1/{\delta}(1+zf^{\prime\prime}/f^{\prime})+1-1/{\delta})(zf^{\prime}/f))$ > ${\zeta}$, ${\mid}z{\mid}$<1. In the present work, the sucient conditions on ${\lambda}(t)$ are investigated, so that the non-linear integral transform $V^{\delta}_{\lambda}(f)(z)=\({\large{\int}_{0}^{1}}{\lambda}(t)(f(tz)/t)^{\delta}dt\)^{1/{\delta}}$, ${\mid}z{\mid}$ < 1, carries the fuctions from $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ into $C_{\delta}({\zeta})$. Several interesting applications are provided for special choices of ${\lambda}(t)$. These results are useful in the attempt to generalize the two most important extremal problems in this direction using duality techniques and provide scope for further research.