• Geomechanics and Engineering
• /
• 제19권5호
• /
• pp.463-472
• /
• 2019

The mode perturbation method (MPM) is suitable and efficient for solving the eigenvalue problem of a nonuniform soil deposit whose property varies with depth. However, results of the MPM do not always converge to the exact solution, when the variation of soil deposit property is discontinuous. This discontinuity is typical because soil is usually made up of sedimentary layers of different geologic materials. Based on the energy integral of the variational principle, a new mode perturbation method, the energy-based mode perturbation method (EMPM), is proposed to address the convergence of the perturbation solution on the natural frequencies and the corresponding mode shapes and is able to find solution whether the soil properties are continuous or not. First, the variational principle is used to transform the variable coefficient differential equation into an equivalent energy integral equation. Then, the natural mode shapes of the uniform shear beam with same height and boundary conditions are used as Ritz function. The EMPM transforms the energy integral equation into a set of nonlinear algebraic equations which significantly simplifies the eigenvalue solution of the soil layer with variable properties. Finally, the accuracy and convergence of this new method are illustrated with two case study examples. Numerical results show that the EMPM is more accurate and convergent than the MPM. As for the mode shapes of the uniform shear beam included in the EMPM, the additional 8 modes of vibration are sufficient in engineering applications.

• 한국음향학회지
• /
• 제7권4호
• /
• pp.22-30
• /
• 1988

이 논문에서는 무한 격리벽내의 가장자리가 고정된 원형평판으로부터의 음압복사를 FFT 기법을 이용하여 계산하였다. 음장은 컴퓨터 계산시간을 절약하기 위해 Rayleigh integral 을 직접 수치해석적으로 구하는 대신에 공간영역에서 2차원 FFT 방법을 이용하였다. 그 결과 1/200의 시간을 절약할 수 있었다. FET방법은 원형평판형상 뿐만아니라 어떤 형상에도 적용 가능하며 복잡한 형상의 근거리 및 원거리 음장을 예측하는데 상당히 유효하다.

• Journal of applied mathematics & informatics
• /
• 제36권1_2호
• /
• pp.1-14
• /
• 2018

In this paper, we prove the existence, uniqueness and stability of solution for some nonlinear functional-integral equations by using generalized coupled Lipschitz condition. We prove a fixed point theorem to obtain the mentioned aim in Banach space $X=C([a,b],{\mathbb{R}})$. As application we study some volterra integral equations with linear, nonlinear and single kernel.

• 한국전자파학회논문지
• /
• 제16권10호
• /
• pp.982-988
• /
• 2005

본 논문에서는 모드 변환기나 필터, 매칭 구조가 모두 연결되어 있는 개구면 안테나의 특성을 예측을 위해 급전 부분에 전이 구조가 붙어 있는 원형 개구면 안테나의 해석적인 산란 해를 제시한다. 개구면의 모양이 원형이기 때문에 길이가 짧고 반지름이 다른 원형 도파관이 연결되어 있는 구조로 모델링하여 안테나를 해석했다. 안테나의 해석에서 급전 도파관과 개구면 사이의 영역은 일반화된 산란 행렬을 이용하여 전기장과 자기장을 나타냈고, 개구면에서 복사되는 전기장과 자기장은 적분 변환을 이용하여 나타내어 전체 구조를 해석했다. 여기서 필요한 산란 행렬과 적분 변환은 모두 해석적으로 계산 가능하고, 엄밀한 해이므로 안테나의 반사 특성, 복사 특성 등을 정확하게 예측 가능하다.

• Journal of Advanced Marine Engineering and Technology
• /
• 제29권5호
• /
• pp.509-518
• /
• 2005

Liquid film thickness in laminar film condensation for flow over a flat plate generally is so thin that both fluid acceleration and thermal convection within the liquid film can be neglected. An integral solution method is proposed to solve the conjugate problems of laminar film condensation and heat conduction in a solid wall. It is found that approximate solutions of the governing equations involve four physical parameters to describe the conjugate heat transfer problem for laminar film condensation. It is shown that the effects of interfacial shear. mass transfer and local heat transfer are strongly dependent on the thermo-physical properties of the working fluids and the Jacob number.

• 한국전자파학회:학술대회논문집
• /
• 한국전자파학회 2003년도 종합학술발표회 논문집 Vol.13 No.1
• /
• pp.54-58
• /
• 2003

In this study, the solution of Gel'fand-Levitan-Marchenko integral equation in the inverse scattering problem is efficiently solved for arbitrarily specified spectra pattern which are reflected from the restricted potential. The procedure is based on the successive approach without iterations. This method lessens the truncation errors which plague conventional design schemes using specific windows for reflection coefficients. It is shown that the method is adequate for the synthesis of the continuously varying one-dimensional potential of the nonuniformly distributed dielectric constants.

• 대한기계학회논문집A
• /
• 제20권7호
• /
• pp.2167-2173
• /
• 1996

An approximate weight function technique using the indirect boundary integral equation has been presented for the analysis of stress intensity foactors(SIFs) of a thick pipe. One-term boundary integral was introduced to represent the crack surface displacement field for the displacement based weight function technique. An explicit closed-form SIF solution applicable to symmetric cracked pipes without any modification of the solution including both circumferential and radial cracks has been derived. The necessary information in the analysis is two or three reference SIFs. In most cases the SIF solution were in good agreement with those available in the literature.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제24권1호
• /
• pp.93-102
• /
• 2020

The concept of temperature distribution in inhomogeneous semi-infinite solids is examined by making use of direct integration method. The analysis is done on the solution of the in-plane steady state heat conduction problem under certain boundary conditions. The method of direct integration has been employed, which is then reduced to Volterra integral equation of second kind, produces the explicit form analytical solution. Using resolvent- kernel algorithm, the governing equation is solved to get present solution. The temperature distribution obtained and calculated numerically and the relation with distribution of heat flux generated by internal heat source is shown graphically.

• Journal of applied mathematics & informatics
• /
• 제30권3_4호
• /
• pp.463-475
• /
• 2012

In this work, we investigate solving two-dimensional nonlinear Volterra integral equations of the first kind (2DNVIEF). Here we convert 2DNVIEF to the two-dimensional linear Volterra integral equations of the first kind (2DLVIEF) and then we solve it by using operational approach of the Tau method. But for solving the 2DLVIEF we convert it to an equivalent equation of the second kind and then by giving some theorems we formulate the operational Tau method with standard base for solving the equation of the second kind. Finally, some numerical examples are given to clarify the efficiency and accuracy of presented method.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제22권2호
• /
• pp.125-136
• /
• 2018

In this article, a homotopy perturbation transform method (HPTM) and the Laplace transform combined with Taylor expansion method are presented for solving Volterra integral equations with a convolution kernel. The (HPTM) is innovative in Laplace transform algorithm and makes the calculation much simpler while in the Laplace transform and Taylor expansion method we first convert the integral equation to an algebraic equation using Laplace transform then we find its numerical inversion by power series. The numerical solution obtained by the proposed methods indicate that the approaches are easy computationally and its implementation very attractive. The methods are described and numerical examples are given to illustrate its accuracy and stability.