• Steel and Composite Structures
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• v.43 no.2
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• pp.185-200
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• 2022

A Closed-form solution for dynamic response of a functionally graded (FG) nonlocal nanobeam due to action of moving harmonic load is presented in this paper. Due to analyzing in small scale, a nonlocal elasticity theory is utilized. The governing equation and boundary conditions are derived based on the Euler-Bernoulli beam theory and Hamilton's principle. The material properties vary through the thickness direction. The harmonic moving load is modeled by Delta function and the FG nanobeam is simply supported. Using the Laplace transform the dynamic response is obtained. The effect of important parameters such as excitation frequency, the velocity of the moving load, the power index law of FG material and the nonlocal parameter is analyzed. To validate, the results were compared with previous literature, which showed an excellent agreement.

• Progress in Superconductivity and Cryogenics
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• v.10 no.4
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• pp.43-45
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• 2008

The thermal characteristics of the helium circulation by a cryocooler are presented. This study is motivated mainly by our recent development of a closed-loop cooling system for Cyclotron K120 superconducting magnets without any replenishment of the cryogen. A channel is attached on the outer surface of the magnet form and the liquid helium passes through inside of the channel in order to cool the super conducting coils indirectly. A two-stage cryocooler as a heat sink is located at the top to recondense helium coming from the superconducting magnet form. The heat transfer in the natural circulation loop is discussed and the main dimensions of cooling system are determined.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.6
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• pp.145-151
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• 1995

The first-order Taylor series expansion can be evaluated analytically from the formulated symbolic nonlinear dynamic equations. A closed-form linear dynamic euation is derived about a nominal trajectory. The state space representation of the linearized dynamics can be derived easily from the closed-form linear dynamic equations. But manual symbolic expansion of dynamic equations and linearization is tedious, time-consuming and error-prone. So it is desirable to manipulate the procedures using a computer. In this paper, the analytic linearization is performed using the symbolic language MATHEMATICA. Two examples are given to illustrate the approach anbd to compare nonlinear model with linear model.

• The Pure and Applied Mathematics
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• v.30 no.2
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• pp.131-138
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• 2023

The aim of this note is to provide two new and interesting closed-form evaluations of the generalized hypergeometric function ₅F₄ with argument $\frac{1}{256}$. This is achieved by means of separating a generalized hypergeometric function into even and odd components together with the use of two known sums (one each) involving reciprocals of binomial coefficients obtained earlier by Trif and Sprugnoli. In the end, the results are written in terms of two interesting combinatorial identities.

• The Journal of Engineering Geology
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• v.32 no.1
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• pp.1-12
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• 2022

Based on the extended spatial mobilization plane (SMP) criterion, we present an elastic-brittle-plastic solution for an axisymmetric cylindrical tunnel. The influences of the intermediate principal compressive stress and material strain-softening behavior are considered. Closed-form formulas for the critical support force, radius of plastic zone, and distributions of stress and displacement in surrounding rock are proposed. The elastic-plastic solution based on SMP is compared with the Kastner solution to verify the credibility of the obtained elastic-plastic solution. The elastic-brittle-plastic solution following the SMP criterion and the current solution based on the Mohr-Coulomb criterion are also compared. The rock strain-softening rate and the intermediate principal stress affect the stability of the surrounding rock. The results provide guidance for optimizing the design of support systems for tunnels.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.135-144
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• 2005

We consider the stochastic differential inclusion of the form $dX_t{\in}{\sigma}(t, X_t)dB_t+b(t, X_t)dt$, where ${\sigma}$, b are set-valued maps, B is a standard Brownian motion. We prove that the set of solutions is closed.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.3
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• pp.142-147
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• 2003

We consider a single-input-single-output nonlinear system which can be represented in a normal form. The nonlinear system has a modeling uncertainties including the input coefficient uncertainty. A high-gain observer is used to estimate the states variables to reject a modeling uncertainty. A globally bounded output feedback integral sliding mode control is proposed to stabilize the closed loop system. The proposed integral sliding mode control can asymptotically stabilize the closed loop system in the presence of input coefficient uncertainty.

• Bulletin of the Korean Chemical Society
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• v.23 no.7
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• pp.971-984
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• 2002

The multichannel quantum defect theory (MQDT) is reformulated into the form of the configuration mixing (CM) method using the geometrical construction of the S matrix developed for the system involving two open and one closed channels. The reformulation is done by the phase renormalization method of Giusti-Suzor and Fano. The rather unconventional short-range reactance matrix K whose diagonal elements are not zero is obtained though the Lu-Fano plot becomes symmetrical. The reformulation of MQDT yields the partial cross section formulas analogous to Fano's resonance formula, which has not easily been available in other's work.

• Proceedings of the Korean Magnestics Society Conference
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• 1998.05a
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• pp.132-133
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• 1998

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.171-175
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• 1992

In this paper, we derive the optimal input-constrained control law which minimizes predictive control objective function subject to input constraints. In order to obtain the closed form of control law, three suboptimal methods are proposed and evaluated by simulation.