• Transactions on Control, Automation and Systems Engineering
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• v.2 no.2
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• pp.140-148
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• 2000

This paper presents iterative schemes and continuation schemes for designing robust controllers which stabilize dynamic systems having bounded parametric uncertainties. Utilizing results of the cheap control problem, some existence conditions of the robust controller are obtained, which are different from the matching conditions. continuation schemes are used to overcome the divergence problem of iterative schemes. The roust controller design method is extended to nonlinear system ans easily implementable series solution is also obtained. Results are illustrated with simple examples.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.781-795
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• 2020

In this paper, we obtain an analytical solution for an unsolved definite integral RC (m, n) from a 1915 paper of Srinivasa Ramanujan. We obtain our solution using the hypergeometric approach and an infinite series decomposition identity. Also, we give some generalizations of Ramanujan's integral RC (m, n) defined in terms of the ordinary hypergeometric function 2F3 with suitable convergence conditions. Moreover as applications of our result we obtain nine new infinite summation formulas associated with the hypergeometric functions 0F1, 1F2 and 2F3.

• ETRI Journal
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• v.35 no.5
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• pp.939-942
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• 2013

We provide a new solution for the projective reconstruction problem based on coupled line cameras (CLCs) and their geometric properties. The proposed solution is composed of a series of optimized steps, and each step is more efficient than those of the initial solution proposed in [1]. We also give a new determinant condition for rectangle determination, which leads to less ambiguity in implementation. The key steps of the proposed solution can be represented with more compact analytic equations due to the intuitive geometric interpretations of the projective reconstruction problem based on CLCs: the center of projection corresponds to the intersection point of the two solution circles of each line camera involved.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.458-463
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• 2000

The mechanical structures generally have discontinuous parts such as the cracks, notches and holes owing to various reasons. In this paper, in order to analyze effectively these singularity problems using the finite element method, a mixed analysis method which an analytical solution and finite element solutions are simultaneously used is newly proposed. As the analytical solution is used in the singularity region and the finite element solutions are used in the remaining regions except this singular zone, this analysis method reasonably provides for the numerical solution of a singularity problem. Through various numerical examples, it is shown that the proposed analysis method is very convenient and gives comparatively accurate solution.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.17 no.10
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• pp.946-949
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• 2007

This paper discusses the lateral vibration of a beam with boundary condition of one end fixed and the other end free. The uniform beam has a solution by summation of some simple exponential functions. But if its shape is not uniform, its solution could be by Bessel's function or mathematical solution could not exist. Even if the solution of Bessel's function exists, as Bessel function is a series function, we must get the solution by numerical method. Author had proposed the solution of the matrix method by Ritz's method and a new mode shape function, and had earned the good results for a wedge beam. Hereby a vibration analysis for the tapered beam with circle cross section was executed, and so good results were showed.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05a
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• pp.79-86
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• 1998

The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized. In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of applications to the NEACRP PWR rod ejection benchmark problem.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.727-740
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• 2006

A simple plane-strain solution is derived in this paper for the functionally graded multilayered isotropic elastic cylinder under static deformation. The solution is obtained using method of separation of variables and is expressed in terms of the summation of the Fourier series in the circumferential direction. While the solution for order n = 0 corresponds to the axisymmetric deformation, that for n = 2 includes the special deformation frequently utilized in the upper and lower bounds analysis. Numerical results for a three-phase cylinder with a middle functionally graded layer are presented for both axisymmetric (n = 0) and general (n = 2) deformations, under either the traction or displacement boundary conditions on the surface of the layered cylinder. The solution to the general deformation case (n = 2) is further utilized for the first time to find the upper and lower bounds of the effective shear modulus of the layered cylinder with a functionally graded middle layer. These results could be useful in the future study of cylindrical composites where FGMs and/or multilayers are involved.

• Journal of the Korean Society of Safety
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• v.19 no.2
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• pp.21-25
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• 2004

This study deals with the characteristics of wire-cut EDM(Electrical Discharge Machining)process in aluminum alloys. Besides 2 series and 7 series of aluminum alloys for aerospace applications, porous aluminum is tested, which is used for sound absorbing matherial and interior and exterior material of building. Jinyoung JW-30 wire cutting machine was used in this experiment. Tap wate passed a filter and ionization was used as the discharging solution. An immerision method was applied as a cooling method because it separates chips effectively and machinability is good even with low value of electric current. The speed of fabrication was estimated by measuring the travel distance of the work piece and time spent for the movement. As pulse-on-time increased the fabrication speed decreased. On the other hand, as peak voltage of peak current increased the fabrication speed increased. In general 7075 aluminum alloy resulted in higher fabrication speed.

• Structural Engineering and Mechanics
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• v.61 no.4
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• pp.453-461
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• 2017

This paper presents the series multiple tuned mass dampers (STMDs) to suppress the resonant vibrations of railway bridges under the passage of high-speed trains (HSTs). A STMD device consisting of two spring-mass-damper units connected each other in series is installed on the bridge. In solution, bridge is modeled as a simply-supported Euler-Bernoulli beam with constant cross-section, and vehicle is simulated as a series of moving forces with constant speed. By the assumed mode method, the governing equations of motion of the beam-TMD device coupled system traversed by a moving train are obtained. The optimum values for the parameters of the STMD device are obtained for the criterion based on the minimization of the maximum dynamic displacement of the beam at its midspan. Single TMD and multiple TMDs in parallel are also considered for demonstration of the STMD device's performance. The results show that STMDs are effective in bridge vibration suppression and robust to parameters' change in the main system and the absorber itself.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.4
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• pp.283-300
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• 2019

In this paper, we propose a new semi-analytic approach based on the generalized Taylor series for solving nonlinear differential equations of fractional order. Assuming the solution is expanded as the generalized Taylor series, the coefficients of the series can be computed by solving the corresponding recursive relation of the coefficients which is generated by the given problem. This method is called the generalized differential transform method(GDTM). In several literatures the standard GDTM was applied in each sub-domain to obtain an accurate approximation. As noticed in [19], however, a direct application of the GDTM in each sub-domain loses a term of memory which causes an inaccurate approximation. In this work, we derive a new recursive relation of the coefficients that reflects an effect of memory. Several illustrative examples are demonstrated to show the effectiveness of the proposed method. It is shown that the proposed method is robust and accurate for solving nonlinear differential equations of fractional order.