• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.85-89
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• 2001

The problem of the transient interaction of a plane acoustic shock wave which has an infinitely steep wave front with a cylindrical or spherical elastic shell has been studied analytically from early fifties based on the integral transform and series solution techniques. Huang adopted an inverse Laplace transform, and used a finite number of terms of the infinite series expansion of the equations for the shells. In the 1990s, the results have been used by many authors for validation of computer codes. The object of this paper is to discuss the interaction between a moving source and submerged spherical shells. Since the center of source is moving the first contact location between the waves and shell changes depending on the source velocity and distance. These are considered in the analysis. Furthermore, constant source strength and decreasing strength are considered in the analysis. Radial velocities at several locations on the structure are obtained and the results are discussed.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.8
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• pp.415-422
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• 2000

This paper presents a new algorithm for hierarchical optimal control of nonlinear systems. The proposed method is simple because the solutions are obtained by only exchanging informations of coefficient vector based on interaction prediction principle and FWT(fast Walsh transform) in upper and lower level. Since we solve two point boundary problem with Picard's iterative method and the backward integral operational matrix of Walsh function to obtain the optimal vector of each independent subsystem, the algorithm is simple and its operation is fast without inverse matrix and kronecker product operation. In simulation, the proposed algorithm's usefulness is proved by comparison with the global optimal control methods.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.601-606
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• 1999

A Walsh function method is proposed in this report for the analysis and optimal control of linear time-delay systems, which is based on the Picard's iterative approximation and fast Walsh transformation. In this research, the following results are obtained: 1) The differential and integral equation can be solved by transforming into a simple algebraic equation as it was possible with the usual orthogonal function method: 2) General orthogonal function methods require usage of Walsh operational matrices for delay or advance and many calculations of inverse matrices, which are not necessary in this method. Thus, the control problems of linear time-delay systems can be solved much faster and readily.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.441-457
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• 2005

An analytical method is presented to solve the problem of transient wave propagation in a transversely isotropic piezoelectric hollow sphere subjected to thermal shock and electric excitation. Exact expressions for the transient responses of displacements, stresses, electric displacement and electric potentials in the piezoelectric hollow sphere are obtained by means of Hankel transform, Laplace transform, and inverse transforms. Using Hermite non-linear interpolation method solves Volterra integral equation of the second kind involved in the exact expression, which is caused by interaction between thermo-elastic field and thermo-electric field. Thus, an analytical solution for the problem of transient wave propagation in a transversely isotropic piezoelectric hollow sphere is obtained. Finally, some numerical results are carried out, and may be used as a reference to solve other transient coupled problems of thermo-electro-elasticity.

• The Journal of the Acoustical Society of Korea
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• v.27 no.3
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• pp.140-148
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• 2008

In this study, a numerical method for a time-domain acoustic wave backscattering analysis is established based on a physical optics and a Fourier transform. The frequency responses of underwater targets are calculated based on physical optics derived from the Kirchhoff-Helmholtz integral equation by applying Kirchhoff approximation and the time-domain signals are simulated taking inverse fast Fourier transform to the obtained frequency responses. Particularly, the adaptive triangular beam method is introduced to calculate the areas impinged directly by acoustic incident wave and the virtual surface concept is adopted to consider the multiple reflection effect. The numerical analysis result for an acoustic plane wave field incident normally upon a square flat plate is coincident with the result by the analytic time-domain physical optics derived theoretically from a conventional physical optics. The numerical simulation result for a hemi-spherical end-capped cylinder model is compared with the measurement result, so that it is recognized that the presented method is valid when the specular reflection effect is predominant, but, for small targets, gives errors due to higher order scattering components. The numerical analysis of an idealized submarine shows that the established method is effectively applicable to large and complex-shaped underwater targets.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.19 no.4
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• pp.427-435
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• 2008

In this paper, a stable marching-on in time(MOT) method with a time domain combined field integral equation(CFIE) is presented to obtain the transient scattering response from arbitrarily shaped three-dimensional conducting bodies. This formulation is based on a linear combination of the time domain electric field integral equation(EFIE) with the magnetic field integral equation(MFIE). The time derivatives in the EFIE and MFIE are approximated using a central finite difference scheme and other terms are averaged over time. This time domain CFIE approach produces results that are accurate and stable when solving for transient scattering responses from conducting objects. Numerical results with the proposed MOT scheme are presented and compared with those obtained from the conventional method and the inverse discrete Fourier transform(IDFT) of the frequency domain CFIE solution.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1105-1127
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• 2013

Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 <; t_1 <{\ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{\ldots},(v_r,x)){\int}_{L_2}_{[0,t]}\exp\{i(v,x)\}d{\sigma}(v)$ for $x{\in}C[0,t]$, where $\{v_1,{\ldots},v_r\}$ is an orthonormal subset of $L_2[0,t]$, $f_r{\in}L_p(\mathbb{R}^r)$, and ${\sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.

• Journal of KSNVE
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• v.9 no.4
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• pp.778-784
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• 1999

A method for obtaining the motion of an impact system whose primary and secondary system are composed of lumped masses, springs and dampers, and all the contacts are made through spring and damping elements is presented. The frequency response functions derived from the equations of motion and the impulse response functions obtained from the inverse Fourier transform of the derived frequency response functions are used for the calculation of the system responses. The procedure developed for the calculation of displacements and force time-histories was based on the convolution integrals of impulse response functions and forces applied to the systems. Time histories of displacements and contact forces are obtained for the case where a random excitation is applied to a point in the system. Impact statistics such as contact forces and the time between impacts calculated from those time histories is presented.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.7
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• pp.1-7
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• 1989

For H-polarized incident plane wave, an exact integral expression for the scattered field by an inversely tapered resistive half plane is obtained by using Kontorovich-Lebedev transform. Uniform asymptotic results available for all angles are obtained, and non-uniform asymptotic results which provide the ray-optical interpretation of the calculated scattered field are also obtained. The edge diffraction patterns for several values of inverse proportionality of resistivity are shown. We find out that the results are in agreement with physical reasoning.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1999.04a
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• pp.143-150
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• 1999

Elastic wave propagation in a multilayered elastic half-plane is studied by using the Cagniard-de Hoop method. After the unknowns are expressed in terms of the reflection and transmission coefficients in the in terms of the reflection and transmission coefficients in the integral-transformed domains they are assmbled to form the global matrix equation. The inverse Laplace transform of each term is done by applying the Cagniard-de Hoop methods. As a numerical example a four-layered half-plane is considered where a point source is applied to the first layer. The method described in the present study can be used in checking other numerical methods such as FDM.