• 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.

• 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.

• East Asian mathematical journal
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• v.35 no.1
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• pp.23-30
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• 2019

Since Mittag-Leffler introduced the so-called Mittag-Leffler function, a number of its extensions have been investigated due mainly to their applications in a variety of research subjects. Shukla and Prajapati presented a lot of formulas involving a generalized Mittag-Leffler function in a systematic manner. Motivated mainly by Shukla and Prajapati's work, we aim to investigate a generalized multi-index Mittag-Leffler function and, among possible numerous formulas, choose to present several formulas involving this generalized multi-index Mittag-Leffler function such as a recurrence formula, derivative formula, three integral transformation formulas. The results presented here, being general, are pointed out to reduce to yield relatively simple formulas including known ones.

• Journal of the Institute of Convergence Signal Processing
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• v.4 no.4
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• pp.47-51
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• 2003

Due to the asymptotic property, deadbeat control which is well used in digital control system can not be applied to the continuous time system. But recently by use of the finite Laplace Transform to transfer function and establishment of some settling conditions, CDBC(Continuous time Deadbeat Control) is studied. For CDBC design, transfer function is constituted with delay elements and then order and interpolation conditions are derived. In other way, digital deadbeat controller is implemented and it's output is changed to continuous type by smoothing elements. In this paper multirate sampling is used and so inner controller is sampled faster than output feedback loop. And End order smoothing elements is placed to the output of digital deadbeat controller. By the multirate sampling overall output response is improved. The controller is impleneted as a serial integral compensator in the forward path and a local feedback compensator introduced into the outpute feedback loop. Matlab Simulink is used for simulation.

• The Korean Journal of Applied Statistics
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• v.27 no.3
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• pp.397-406
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• 2014

The minimum density power divergence estimation has been a popular topic in the field of robust estimation for since Basu et al. (1988). The minimum density power divergence estimator has strong robustness properties with the little loss in asymptotic efficiency relative to the maximum likelihood estimator under model conditions. However, a limitation in applying this estimation method is the algebraic difficulty on an integral involved in an estimation function. This paper considers a minimum density power divergence estimation method with approximated divergence avoiding such difficulty. As an example, we consider the normal-exponential convolution model introduced by Bolstad (2004). The estimated divergence in this case is too complicated; consequently, a Laplace approximation is employed to obtain a manageable form. Simulations and an empirical study show that the minimum density power divergence estimators based on an approximated estimated divergence for the normal-exponential model perform adequately in terms of bias and efficiency.

• Ocean Systems Engineering
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• v.1 no.4
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• pp.355-372
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• 2011

Based on the fully nonlinear velocity potential theory, the liquid sloshing in a three dimensional tank under random excitation is studied. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing scheme, B-spline curve, is applied to both the longitudinal and transverse directions of the tank to eliminate the possible saw-tooth instabilities. When the tank is undergoing one dimensional regular motion of small amplitude, the calculated results are found to be in very good agreement with linear analytical solution. In the simulation, the normal standing waves, travelling waves and bores are observed. The extensive calculation has been made for the tank undergoing specified random oscillation. The nonlinear effect of random sloshing wave is studied and the effect of peak frequency used for the generation of random oscillation is investigated. It is found that, even as the peak value of spectrum for oscillation becomes smaller, the maximum wave elevation on the side wall becomes bigger when the peak frequency is closer to the natural frequency.

• Honam Mathematical Journal
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• v.2 no.1
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• pp.1-8
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• 1980

논문(論文)[3] (본(本) 논문(論文) 제1부(第1部))에서 미분가능다양체(微分可能多樣體) M 위의 (n-1)차(次) 미분형식(微分型式) ${\beta}^{(n-1)}$이 Compact인 Carrier를 가지면 ${\int}d{\beta}^{(n-1)}=0$이며, (p-1)차(次) 미분형식(微分型式) ${\beta}^{(p-1)}$과 p차(次) 미분가능쇄(微分可能쇄鎖) $C^{(p)}=\Sigma\limits_ik_iS_i{^{(p)}}$에 대(對)하여 ${\int\limits_{c^{(p)}}}d{\beta}^{(p-1)}={\int\limits_{{\partial}{c}^{(p)}}}{\beta}^{(p-1)}$이 성립(成立) (Stokes 정리(定理)의 일반화(一般化))⋯등(等) M위의 적분(積分)에 관한 여러 가지 성질(性質)들을 구명(究明)하였다. 이 성질(性質)들을 토태(土台)로 하여 본(本) 논문(論文)에서는; 제2절(第2節)에서 미분가능다양체(微分可能多樣體) M위의 Lie 도함수(導函數)의 정의(定義)와 Lie적분(微分)에 관(關)한 여러가지 성질(性質)들을 고찰(考察)하고, 제3절(第3節)에서 div X와 Laplace 작용소(作用素) ${\Delta}f$의 정의(定義) 및 실(實) n차원(次元) 가부호미분가능(可符號微分可能) 다양체(多樣體) M 위에서의 divX와 ${\Delta}f$의 적분(積分)에 관(關)한 성질(性質), 즉(卽) $V=\sqrt{{\mid}g{\mid}}dx^1{\Lambda}{\cdots}{\Lambda}dx^n{\in}A^n(M)$에 대(對)하여 $$\int_MdivXV\limits=\int_M{\Delta}fv=0$$인 관계(關係)가 성립(成立)함을 구명(究明)한다. (정리(定理) 3.3)

• Ocean Systems Engineering
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• v.4 no.2
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• pp.83-97
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• 2014

Wave propagation in a three-dimensional (3D) fully nonlinear numerical wave tank (NWT) is studied based on velocity potential theory. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing algorithm, B-spline, is applied to eliminate the possible saw-tooth instabilities. The artificial wave speed employed in MTF (multi-transmitting formula) approach is investigated for fully nonlinear wave problem. The numerical results from incorporating the damping zone (DZ), MTF and MTF coupled DZ (MTF+DZ) methods as radiation condition are compared with analytical solution. An effective MTF+DZ method is finally adopted to simulate the 3D linear wave, second-order wave and irregular wave propagation. It is shown that the MTF+DZ method can be used for simulating fully nonlinear wave propagation very efficiently.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.3 no.3
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• pp.176-183
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• 1991

In this paper. boundary element method is applied to the analysis of nonlinear free surface wave. A particular concern is given to the treatment of the open boundaries at the in-flow boundary and out-flow boundary, which uses the mass-flux and energy-flux considering the continuity of fluid. By assuming the fluid to be inviscid and incompressible and the flow to be irrotational. the problem is formulated mathematically as a two-dimentional nonlinear problem in terms of a velocity potential. The equation(Laplace equation) and the boundary conditions are transformed into two boundary integral equations. Due to the nonlinearity of the problem. the incremental method is used for the numerical analysis. Numerical results obtained by the present boundary element method are compared with those obtained by the finite element method and also with experimental values.

• Geomechanics and Engineering
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• v.21 no.3
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• pp.279-288
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• 2020

The permeation grouting is a commonly used technique to improve the engineering geology condition of the soft ground. It is of great significance to predict the permeation range of the grout so as to ensure the effects of grouting. This paper conducts a theoretical analysis of jet-grouting effects in ground improvement and rotary grouting pile installation by utilizing deformation-permeation coupled poroelastic solutions based on Biot's theory and Laplace-Fourier integral transform technique. The exponential function and the intermittent trigonometric function are chosen to represent time-dependent grouting pressure usually encountered in ground improvement and rotary grouting pile installation process, respectively. The results, including the radial displacement, the hoop stress, the excess pore fluid pressure, the radial discharge, and the permeation radius of grout, are presented for different grouting time, radial positions and grouting lengths. Parametric study is conducted to explore the effects of variation of the exponent in the exponential grouting pressure-time relationship on grouting-induced responses. It is expected that the proposed solutions can be used to estimate the permeation range of grouting in ground improvement and rotary grouting pile installation.