• 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.

• The Journal of the Acoustical Society of Korea
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• v.28 no.3
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• pp.174-186
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• 2009

When we apply a propagation model to the ocean with boundaries, we can calculate reflected wave using reflection coefficient suggested by Rayleigh assuming the boundaries are flat. But boundaries in ocean such as sea surface and sea bottom have an irregular rough surface. To calculate the reflection loss for an irregular boundary, it is needed to compute the coherent reflection coefficient based on an experimental formula or scattering theory. In this article, we derive the coherent reflection coefficients for a fluid-fluid interface using perturbation theory, Kirchhoff approximation and small-slope approximation respectively. Based on each formula, we can calculate coherent reflection coefficients for a rough sea surface or sea bottom, and then compare them to the Rayleigh reflection coefficient to analyze the reflection loss for a random rough surface. In general, the coherent reflection coefficient based on small-slope approximation has a wide valid region. Comparing it with the coherent reflection coefficients derived from the Kirchhoff approximation and perturbation theory, we discuss a valid region of them.

• The Journal of the Acoustical Society of Korea
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• v.20 no.4
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• pp.81-86
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• 2001

126-kHz bistatic sea surface scattering measurements were conducted in the shallow waters off the east coasts of Korea. The range from source to receiver was altered to change the scattering angle at the grazing angles of 38％ and 52％ . Unlike bottom scattering signal, the arrival time and the amplitude of sea surface scattering signals were varied due to the fluctuation of sea surface. The measured forward scattering strengths were compared to model predictions of Kirchhoff approximation and small slope approximation. In overall, the tendency of the scattering strengths showed reasonable agreement among the experimental data, Kirchhoff approximation, and small slope approximation.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.1062-1073
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• 2007

Acoustic Target Strength (TS) is a major parameter of the active sonar equation, which indicates the ratio of the radiated intensity from the source to the re-radiated intensity by a target. In developing a TS equation, it is assumed that the radiated pressure is known and the re-radiated intensity is unknown. This research provides a TS equation for polygonal plates, which is applicable to near field acoustics. In this research, Helmholtz-Kirchhoff formula is used as the primary equation for solving the re-radiated pressure field; the primary equation contains a surface (double) integral representation. The double integral representation can be reduced to a closed form, which involves only a line (single) integral representation of the boundary of the surface area by applying Stoke's theorem. Use of such line integral representations can reduce the cost of numerical calculation. Also Kirchhoff approximation is used to solve the surface values such as pressure and particle velocity. Finally, a generalized definition of Sonar Cross Section (SCS) that is applicable to near field is suggested. The TS equation for polygonal plates in near field is developed using the three prescribed statements; the redection to line integral representation, Kirchhoff approximation and a generalized definition of SCS. The equation developed in this research is applicable to near field, and therefore, no approximations are allowed except the Kirchhoff approximation. However, examinations with various types of models for reliability show that the equation has good performance in its applications. To analyze a general shape of model, a submarine type model was selected and successfully analyzed.

• 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.

• 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.24 no.4
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• pp.354-361
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• 2004

This Paper describes a crack scattering model for SH wave based on the boundary integral equation(BIE) method, where the fundamental unknown is crack opening displacement(COD). When a time harmonic plane wave was incident on a 2-D isolated crack (slit) of width 2a, the COD distributions were numerically calculated as a function of ka. The calculated COD agreed well with results obtained with other methods. The far-field scattering amplitude, which completely characterizes the flaw response, was calculated in two ways. The Kirchhoff approximation and the BIE-COD exact formulation were compared in terms of incidence angle and frequency ka in a pulse-echo mode. Maximum response was obtained for both methods at the specular reflection direction. Away from the specular direction, the Kirchhoff approximation becomes less accurate. The time domain crack response was also calculated using a band-limited spectrum of center frequency 10 MHz. At oblique incidence to the crack both methods show the existence of an antisymmetric flash points occurring from the crack edge. The Kirchhoff approximation provides an exact time interval between flash points, although it unrealistically gives the same amplitude.

• Geophysics and Geophysical Exploration
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• v.1 no.1
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• pp.8-18
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• 1998

In exploration seismology, the Kirchhoff hyperbola has been successfully used to migrate reflection seismo-grams. The mathematical basis of Kirchhoff hyperbola has not been clearly defined and understood for the application of prestack or poststack migration. The travel time from the scatterer in the subsurface to the receivers (exploding reflector model) on the surface can be a kinematic approximation of Green's function when the source is excited at position of the scatterer. If we add the travel time from the source to the scatterer in the subsurface to the travel time of exploding reflector model, we can view this travel time as a kinematic approximation of the partial derivative wavefield with respect to the velocity or the density in the subsurface. The summation of reflection seismogram along the Kirchhoff hyperbola can be evaluated as an inner product between the partial derivative wavefield and the field reflection seismogram. In addition to this kinematic interpretation of Kirchhoff hyperbola, when we extend this concept to shallow refraction seismic data, the stacking of refraction data along the straight line can be interpreted as a measurement of an inner product between the first arrival waveform of the partial derivative wavefield and the field refraction data. We evaluated the Kirchhoff hyperbola and the straight line for stacking the refraction data in terms of the first arrival waveform of the partial derivative wavefield with respect to the velocity or the density in the subsurface. This evaluation provides a firm and solid basis for the conventional Kirchhoff migration and the straight line stacking of the refraction data.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.189-206
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• 2014

In this paper, we prove the global existence and uniqueness of the dissipative Kirchhoff equation $$u_{tt}-M({\parallel}{\nabla}u{\parallel}^2){\triangle}u+{\alpha}u_t+f(u)=0\;in\;{\Omega}{\times}[0,{\infty}),\\u(x,t)=0\;on\;{\Gamma}_1{\times}[0,{\infty}),\\{\frac{{\partial}u}{\partial{\nu}}}+g(u_t)=0\;on\;{\Gamma}_0{\times}[0,{\infty}),\\u(x,0)=u_0,u_t(x,0)=u_1\;in\;{\Omega}$$ with nonlinear boundary damping by Galerkin approximation benefited from the ideas of Zhang et al. [33]. Furthermore,we overcome some difficulties due to the presence of nonlinear terms $M({\parallel}{\nabla}u{\parallel}^2)$ and $g(u_t)$ by introducing a new variables and we can transform the boundary value problem into an equivalent one with zero initial data by argument of compacity and monotonicity.