• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.71-111
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• 2021

We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence �� from the set of equivalent well-posed two-point boundary conditions to gl(4, ℂ). Using ��, we derive eigenconditions for the integral operator ��M for each well-posed two-point boundary condition represented by M ∈ gl(4, 8, ℂ). Special features of our eigenconditions include; (1) they isolate the effect of the boundary condition M on Spec ��M, (2) they connect Spec ��M to Spec ����,α,k whose structure has been well understood. Using our eigenconditions, we show that, for each nonzero real λ ∉ Spec ����,α,k, there exists a real well-posed boundary condition M such that λ ∈ Spec ��M. This in particular shows that the integral operators ��M, arising from well-posed boundary conditions, may not be positive nor contractive in general, as opposed to ����,α,k.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.05a
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• pp.677-680
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• 2008

The paper deals with the analysis of radiation characteristics of antenna in the multi-layered media structures. The dyadic Green's function for three layer medium is complex because the Green's functions belonging to the kernel of the integral equation are expressed as Sommerfeld integrals, in which surface wave effects are automatically included. When certain condition are met, the integral can be evaluated approximated by the method of Saddle-point integration. In this study, we propose a method to calculate a radiation pattern for several antennas by using the method of Saddle-point integration. Numerical results show how the radiation characteristics are affected by parameter of dielectric media.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.73-91
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• 2005

The application of Green's function in calculation of flow characteristics around submerged and floating bodies due to a regular wave is presented. It is assumed that the fluid is homogeneous, inviscid and incompressible, the flow is irrotational and all body motions are small. Two methods based on the boundary integral equation method (BIEM) are applied to solve associated problems. The first is a low order panel method with triangular flat patches and uniform distribution of velocity potential on each panel. The second method is a high order panel method in which the kernels of the integral equations are modified to make it nonsingular and amenable to solution by the Gaussian quadrature formula. The calculations are performed on a submerged sphere and some floating spheroids of different aspect ratios. The excellent level of agreement with the analytical solutions shows that the second method is more accurate and reliable.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.7 no.2
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• pp.156-162
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• 1995

A numerical method for a 2-D oil boom model considering the flexibility of skirt has been developed The neater is assumed rigid and the skirt is tensioned membrane having a point mass at its end The fluid motion is potential. The kinematic condition which demands the continuity of the displacement is imposed at the joint between the floater and the skirt. The dynamic condition for the point mass is imposed at the bottom end of the skirt. The numerical method is based on the Green's function method in the frame of linear potential theory. It finds it's solution simultaneously from the total system of three equations, integral equation, the equation of motion of the floater and the equilibrium equation of the deformation of the skirt. Integral equation is derived by applying the Green's theorem to radiation potential and Green's function. Proper descretization of those three equations leads to the system of a linear algebraic equation. Due to the flexibility of skirt the motion of floater can be diminished in some range of wave frequency and furthermore the mechanism of resonance of the oil boom can be changed. The motion responses of various oil booms have been compared varying the length of the skirt and the point mass. The numerical method has been validated indirectly from the good correspondence between the motion responses of the flexible skirt model and the rigid skirt model in low frequency limit.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.292-292
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• 2004

There are many difficulties to get the scattered field generated by obstacle which has arbitrary shape or irregular surface impedance by using analytic solution or numerical methods. In this study, we propose experimental method of acoustic scattering holography that can predict the far-field scattered field based on nearfield measurements. First of all, we express scattered field using K-H integral equation and compare the differences of which green's function we use. Also we consider analytic solution of scattered field by infinite cylinder to analysis for the errors due to apply cylinderical holography. So the errors which caused by holography due to frequency (ka) and microphone spacing are also analyzed by numerical simulation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.1317-1322
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• 2001

What changes in the eigen values and eigen functions are produced if the boundary surface S is no longer rigid but has a specific acoustic admittance which may vary from point to point on S. In this paper, changes in eigen values and eigen functions are derived by using Kirchhoff-Helmholtz integral equation. And acoustic potential energy, which is representative measure describing the physical quantity in cavity, is defined. Acoustic potential energy can be divided into primary one and secondary one. Primary one is the acoustic potential energy through unchanged eigen functions, and secondary one is through changed eigen functions. Using these two term, we can find the eigenvalue problem, which gives the control performance when the boundary condition is changed.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.12
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• pp.55-63
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• 1995

By employing the concept of superimposing the induced current on partial scattere roled as a secondary source, matrix Green's function was derived. The procedure in the way of derivation presented here was based on the equivalence principle and the induction theorem and applying moment methods to the resulting electric field integral equation. As examples, the induced current on scatterers consisted of wire/plate conductor, the input impedance and gain patterns of corner reflector antenna were calculated. And computing times required for solving matrix equation were compared with those of conventional method.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.51 no.8
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• pp.375-381
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• 2002

A rigorous analysis of a broad wall slot array is presented. The slot is longitudinal and offset from the center line in the rectangular waveguide. Pertinent integral equations are developed, taking into account finite wall thickness. The mothed of moment with entire basis function is used to solve a pair of coupled-integral equations, derived from the electromagnetic boundary conditions using modified Green's function, to find the tangential electric field on the upper and lower surfaces of the slot. Numerical results for resonant length and scattering parameters of the slots are Presented over a range of offset. Computed results are compared with experimental result.

• Journal of Industrial Technology
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• v.9
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• pp.79-85
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• 1989

In this paper, the static limit of Helmhortz equation is discussed in the analysis of acoustic wave scattering in a waveguide. Boundary integral equation method is used to formulate the scattering process in the exerior of the scatterer and finite element method in the interior of the scatterer. And hybrid Ray-Mode Method is used the provide the Green's function of the waveguide. The proposed algorithm is applied to a sample poblem with arbitrary scatterer in a waveguide. The results are compared with those of Laplace's equation which is the governing equation in the static problems.

• Smart Structures and Systems
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• v.17 no.5
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• pp.753-771
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• 2016

This paper addresses the free and transient responses of a SDOF linear complex stiffness system by making use of the Hilbert transform and the convolution integral. Because the second-order differential equation of motion having the complex stiffness give rise to the conjugate complex eigen values, its time-domain analysis using the standard time integration scheme suffers from the numerical instability and divergence. In order to overcome this problem, the transient response of the linear complex stiffness system is obtained by the convolution integral of a green function which corresponds to the unit-impulse free vibration response of the complex system. The damped free vibration of the complex system is theoretically derived by making use of the state-space formulation and the Hilbert transform. The convolution integral is implemented by piecewise-linearly interpolating the external force and by superimposing the transient responses of discretized piecewise impulse forces. The numerical experiments are carried out to verify the proposed time-domain analysis method, and the correlation between the real and imaginary parts in the free and transient responses is also investigated.