• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.165-182
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• 2003

Toeplitz matrix method and the product Nystrom method are described for mixed Fredholm-Volterra singular integral equation of the second kind with Carleman Kernel and logarithmic kernel. The results are compared with the exact solution of the integral equation. The error of each method is calculated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.111-123
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• 2005

Here, the Fredholm integral equation with Hilbert kernel is solved numerically, using two different methods. Also the error, in each case, is estimated.

• Earthquakes and Structures
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• v.24 no.3
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• pp.217-235
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• 2023

Orthogonal pairs of rollers on concave beds (OPRCB) are a low-cost, low-tech rolling-based isolating system, whose high efficiency has been shown in a previous study. However, seismic performance of OPRCB isolators has only been studied in the two-dimensional (2D) state so far. This is while their performance in the three-dimensional (3D) state differs from that of the 2D state, mainly since the vertical accelerations due to rollers' motion in their beds, simultaneously in two orthogonal horizontal directions, are added up and resulting in bigger vertical inertia forces and higher rolling resistance. In this study, first, Lagrange equations were used to derive the governing equations of motion of the OPRCB-isolated buildings in 3D. Then, some regular shear-type OPRCB-isolated buildings were considered subjected to three-component excitations of far- and near-source earthquakes, and their responses were compared to those of their fixed-base counterparts. Finally, the effects of more realistic modeling and analysis were examined by comparing the responses of isolated buildings in 2D and 3D states. Response histories were obtained by the fourth-order Runge-Kutta-Nystrom method, considering the geometrical nonlinearity of isolators. Results reveal that utilizing the OPRCB isolators effectively reduces the acceleration response, however, depending on the system specifications and earthquake characteristics, the maximum responses of isolated buildings in the 3D state can be up to 40% higher than those in the 2D state.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.5
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• pp.143-150
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• 2021

To develop the technique for predicting the horizontal displacement of a retaining wall induced by an earthquake, an equation of motion that depicts the retaining wall-soil vibrating system was derived. The resulting differential equation was solved using the Runge-Kutta-Nystr?m method. Considering the pre-mentioned derivation process, the analysis procedures for obtaining horizontal displacement induced by an earthquake were programmed. The core algorithm of the displacement-force relationship, which is the main engine of the developed program, was suggested. Considering the results obtained by adopting the developed program to the assumed retaining wall under an earthquake, the relationships between the time-displacement, time-force, and displacement-force were reasonable. According to the results computed by the program, the displacements to the front direction of the wall occurred, and the displacement per cycle converged after some cycles elapsed. Displacements with a natural period were calculated, which showed that the maximum displacement was observed when the natural frequency was slightly different from the excitation frequency rather than the same values of the two frequencies. This happens because the vibrating system was modeled by two springs with different stiffness.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.12
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• pp.1148-1154
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• 2011

In this paper, the radiation properties of a Ka-band Von Karman radome are analyzed by using an IPO(Iterative PO) scheme. Since the operating frequency is very high, and the size of the considered radome is large, a numerical method cannot be directly applied to calculate the properties of the radome such as transmission loss, radome pattern, boresight error, etc. Hence, in this paper, an IPO scheme is used, which can efficiently consider the multiple interaction inside the radome. Also, the IPO scheme is based on the PO scheme, which is efficient and fast in a numerical point of view. The proposed scheme is verified based on Ku-band measurement data, and its feasibility for applicability to a higher frequency simulation is addressed through a simulation at the Ka-band.