• Journal of Ship and Ocean Technology
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• v.1 no.2
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• pp.11-18
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• 1997

The leading edge of a low-drag super-cavitating foil has been made to be thick enough by using a point drag which is supposed to be a linear model of the Kirchhoff lamina. In the present paper, the relation between the point drag and the Kirchhoff lamina is made clear by analyzing the cavity drag of both models and the leading edge radius of the point drag model and the lamina thickness of Kirchhoff\`s profile K. The matched asymptotic expansion is effectively made use of in designing a practical super-cavitating fool which is not only of low drag but also structurally sound. Also it has a distinct leading edge cavity separation point. The cavity foil shapes of trans-cavitating propeller blade sections designed by present method are shown.

• Coupled systems mechanics
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• v.8 no.6
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• pp.537-553
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• 2019

In this paper we present geometrically exact Kirchhoff's initially curved planar beam model. The theoretical formulation of the proposed model is based upon Reissner's geometrically exact beam formulation presented in classical works as a starting point, but with imposed Kirchhoff's constraint in the rotated strain measure. Such constraint imposes that shear deformation becomes negligible, and as a result, curvature depends on the second derivative of displacements. The constitutive law is plasticity with linear hardening, defined separately for axial and bending response. We construct discrete approximation by using Hermite's polynomials, for both position vector and displacements, and present the finite element arrays and details of numerical implementation. Several numerical examples are presented in order to illustrate an excellent performance of the proposed beam model.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.25-32
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• 2004

In this proposed work new finite element model for multi-delaminated plates is proposed. In the current analysis procedures of multi-delaminated plates, plate element based on Mindlin plate theory is used in order to obtain accurate results of out-of-plane displacement of thick plate. And for delaminated region, plate element based on Kirchhoff plate theory is considered. To satisfy the displacement continuity conditions, displacement vector based on Kirchhoff theory is transformed to displacement of transition element. The numerical results show that the effect of delaminations on the modal parameters of delaminated composites plates is dependent not only on the size, the location and the number of the delaminations but also on the mode number and boundary conditions. Kirchhoff based model have higher natural frequency than Mindlin based model and natural frequency of the presented model is closed to Mindlin based model.

• Geophysics and Geophysical Exploration
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• v.5 no.3
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• pp.185-192
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• 2002

We made a study of 3-D migration which could precisely image data of GPR (Ground Penetrating Radar) applied to NDT (Non-Destructive Test) field for the inspection of structural safety. In this study, we obtained 3-D migrated images of important targets in structuresurvey (e.g. steel pipes, cracks) by using 3-D Kirchhoff prestack depth migration scheme developed for seismic data processing. For a concrete model consisting of steel pipe and void, the targets have been well defined with opposite amplitude according to the parameters of the targets. And migrated images using Parallel-Broadside array (XX configuration) have shown higher resolution than those using Perpendicular-Broadside array (YY configuration) when steel pipes had different sizes. Therefore, it is required to analyze the migrated image of XX configuration as well as that of general YY configuration in order to get more accurate information. As the last stage, we chose a model including two steel pipes which cross each other. The upper pipe has been resolved clearly but the lower has been imaged bigger than the model size due to the high conductivity of the upper steel.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.442-445
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• 2004

The acoustic target strength (TS) of submarine is associated with its active detection, positioning and classification. That is, the survivability of submarine depends on its target strength. So it should be managed with all possible means. An anechoic coating to existing submarine or changing of curvature can be considered as major measures to reduce the TS of submarine. It is mainly based on the prediction of its TS. Under this circumstances, a study on the more accurate numerical methods becomes big topic for submarine design. In this paper, Kirchhoff approximation method was adopted as a numerical tool for the physical optics region. Secondly, the scaled models of submarine were built and tested in order to verify its performance. Through the comparison, it was found out that the Kirchhoff approximation method could be good design tool for the prediction of TS of submarine.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.245-252
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• 2006

In this paper we study the uniform decay estimates of the energy for the nonlinear wave equation of Kirchhoff type $$y'(t)-M({\mid}{\nabla}y(t){\mid}^2){\triangle}y(t)\;+\;{\delta}y'(t)=f(t)$$ with the damping constant ${\delta} > 0$ in a bounded domain ${\Omega}\;{\subset}\;\mathbb{R}^n$.

• East Asian mathematical journal
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• v.30 no.3
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• pp.249-258
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• 2014

In this paper, we study uniform exponential stabilization of the vibrations of the Kirchhoff type wave equation with Balakrishnan-Taylor damping and acoustic boundary in a bounded domain in $R^n$. To stabilize the systems, we incorporate separately, the passive viscous damping in the model as like Kang[14]. Energy decay rates are obtained by the uniform exponential stability of solutions by using multiplier technique.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.1
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• pp.45-52
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• 1995

A new Kirchhoff approximation(KA) method was proposed for microwave scttering from randomly rough surfaces. Using the spectral representation of delta function and its sifting theorem, a new KA was formulated directly without any further approximation, and this formulated was used to compute exact backscttering coefficients. The validity of the KA was verified by a numerical method, and this new KA technique was used to evaluate the existing approximated KkA methods; i.t., the zeroth-order and the first-order approximated physical optics(PO) models. It was shown that the first-order approximated PO model has small error than the zeroth-order approximated PO model at low incidence angles and the opposite happens at higher incidence angles. This new KA model can be used to compute exact scattering coefficients in the validity regions of KA and to evaluate other theoretical and numerical models for scattering from randomly rough surfaces.

• Journal of the Korean Society for Nondestructive Testing
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• v.24 no.6
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• pp.559-565
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• 2004

Two different methods were used for the scattering analysis of side-drilled holes(SDH). The scattering models include an explicit model based on the Kirchhoff approximation and the solution of the exact separation of variables. The far-field scattering amplitude was calculated and their time-domain results were compared for the case of shear vertical wave. The exact solution predicts the existence of the creeping wave. The Kirchhoff approximation agreed to the exact solution, except the case of the creeping wave. Two measurement models were introduced to predict the response from the SDHs for the case of immersion, pulse-echo testing. The received voltage was calculated for the case of the shear vertical waves with the incident angle of $45^{\circ}$ to the SDH with the diameter of 1mm, and compared with the experimental results.

• Journal of the Korean Society for Nondestructive Testing
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• v.20 no.2
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• pp.102-109
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• 2000

This paper describes two different theories used to model the scattering of ultrasound by a volumetric flaw and a crack-like flaw. The elastodynamic Kirchhoff approximation (EKA) and the geometrical theory of diffraction (GTD) are applied respectively to a cylindrical cavity and a semi-infinite crack. These methods are known as high frequency approximations. The 2-D elastodynamic scattering problems of a plane wave incident on these model defects are considered and the scattered fields are expressed in terms of the reflection and diffraction coefficients. The ratio of the scattered far field amplitude to the incident wave amplitude is computed as a function of the angular location and compared with the boundary element solutions.