• 대한수학회보
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• 제35권2호
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• pp.345-362
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• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• 한국ITS학회 논문지
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• 제8권3호
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• pp.71-82
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• 2009

As a solution to spectrum under-utilization problem, Cognitive radio (CR) introduces a dynamic spectrum access technology. In the area, one of the most important problems is how secondary users (SUs) should choose between the available channels, which means how to achieve load balancing between channels. We consider spectrum load balancing problem for CR system in frequency domain and especially in time domain. Our objective is to balance the load among the channels and balance the occupied time length of slots for a fixed channel dynamically in order to obtain a user-optimal solution. In frequency domain, we refer to Dynamic Noncooperative Scheme with Communication (DNCOOPC) used in distributed system and a distributed Dynamic Spectrum Load Balancing algorithm (DSLB) is formed based on DNCOOPC. In time domain, Spectrum Load Balancing method with QoS support is proposed based on Dynamic Feed Back theory and Hash Table (SLBDH). The performance of DSLB and SLBDH are evaluated. In frequency domain, DSLB is more efficient compared with existing Compare_And_Balance (CAB) algorithm and gets more throughput compared with Spectrum Load Balancing (SLB) algorithm. Also, DSLB is a fair scheme for all devices. In time domain, SLBDH is an efficient and precise solution compared with Spectrum Load Smoothing (SLS) method.

• Geomechanics and Engineering
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• 제19권5호
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• pp.369-381
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• 2019

The objective of this paper is to study the two dimensional deformation in transversely isotropic thermoelastic medium without energy dissipation due to time harmonic sources using new modified couple stress theory, a continuum theory capable to predict the size effects at micro/nano scale. The couple stress constitutive relationships have been introduced for transversely isotropic thermoelastic medium, in which the curvature tensor is asymmetric and the couple stress moment tensor is symmetric. Fourier transform technique is applied to obtain the solutions of the governing equations. Assuming the deformation to be harmonically time-dependent, the transformed solution is obtained in the frequency domain. The application of a time harmonic concentrated and distributed sources have been considered to show the utility of the solution obtained. The displacement components, stress components, temperature change and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effects of angular frequency are depicted graphically on the resulted quantities.

• 한국구조물진단유지관리공학회 논문집
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• 제11권3호
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• pp.87-94
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• 2007

구조물의 동적해석은 크게 시간영역과 주파수영역해석으로 나눌 수 있다. 시간영역해석은 직접적분법과 모드중첩법 등을 사용하며 주파수영역해석은 DFT법을 적용하고 있다. 일반적으로 DFT법은 주기함수에 대한 응답을 산정할 경우 효과적인 해석방법이지만 비주기함수인 경우 정확한 해석결과를 얻을 수 없어 주기를 크게 하거나 응답을 수정하여 해의 정확성을 향상시키고 있다. 따라서 본 연구는 비주기함수인 이동하중을 받는 구조물에 대해 시간영역과 주파수영역에서 동적응답을 산정하였다. 그 결과 구조물의 자유진동주기를 크게 하거나 응답을 수정하여 DFT법을 적용한다면 주파수영역에서도 충분히 정확한 해석결과를 얻을 수 있을 것으로 판단된다.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2000년도 추계 학술발표회 논문집 Proceedings of EESK Conference-Fall 2000
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• pp.143-150
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• 2000

A physical lumped parameter model is proposed for the time domain analysis of dam-reservoir system. The exact solution of transmitting boundary is derived for a semi-infinite 2-D reservoir of constant depth. The characteristics of the solution are examined in both frequency and the domains. Mass and damping coefficient are obtained from asymptotic behavior of the frequency domain solution. Further refinement to the lumped model is made by approximating the kernel function of the convolution integral in the exact solution. Finally a new physical lumped parameter model is proposed that consists of two masses, a spring and two dampers for each mode. It is demonstrated that new lumped parameter model of transmitting boundary can give excellent results.

• 대한조선학회지
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• 제24권4호
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• pp.9-18
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• 1987

The hydrodynamic radiation forces acting on a ship travelling in waves have been conventionally treated by strip theories or by direct three dimensional approaches, most of which have been formulated in frequency domain. If the forward speed of a ship varies with time, or if its path is not a straight line, conventional frequency domain analysis can no more be used, and for these cases time domain analysis may be used. In this paper, formulations are made in time domain with applications to some problems the results of which are known in frequency domain. And the results of both domains are compared to show the characteristics and validity of time domain solutions. The radiation forces acting on a three dimensional body within the framework of a linear theory. If the linearity of entire system is assumed, radiation forces due to arbitrary ship motions can be expressed by the convolution integral of the arbitrary motion velocity and the so called impulse response function. Numerical calculations are done for some bodies of simple shapes and Series-60[$C_B=0.7$] ship model. For all cases, integral equation techniques with transient Green's function are used, and velocity or acceleration potentials are obtained as the solution of the integral equations. In liner systems, time domain solutions are related with frequency domain solutions by Fourier transform. Therefore time domain solutions are Fourier transformed by suitable relations and the results are compared with various frequency domain solutions, which show good agreements.

• Current Optics and Photonics
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• 제2권3호
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• pp.250-260
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• 2018

A pressure wave created by the photoacoustic effect is affected by the medium and by laser parameters. The effect of these parameters on the generated pressure wave can be seen by solving the photoacoustic wave equation. These solutions which are examined in the time domain and the frequency domain should be considered by researchers in acoustic sensor design. In particular, frequency domain analysis contains significant information for designing the sensor. The most important part of this information is the determination of the operating frequency of the sensor. In this work, the laser parameters to excite the medium, and the acoustic signal parameters created by the medium are analyzed. For the first time, we have obtained solutions for situations which have no frequency domain solutions in the literature. The main focal point in this work is that the frequency domain solutions of the acoustic wave equation are performed and the effects of the frequency analysis of the related parameters are shown comparatively from the viewpoint of using them in acoustic sensor designs.

• Interaction and multiscale mechanics
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• 제6권4호
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• pp.357-375
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• 2013

In this paper, the forced vibration problem of an Euler-Bernoulli beam that is joined with a semi-infinite field of a compressible fluid is considered as a boundary value problem (BVP). This BVP includes two partial differential equations (PDE) and some boundary conditions (BC), which are introduced comprehensively. After that, the closed-form solution of this fluid-structure interaction problem is obtained in the frequency domain. Some mathematical techniques are utilized, and two unknown functions of the BVP, including the beam displacement at each section and the fluid dynamic pressure at all points, are attained. These functions are expressed as an infinite series and evaluated quantitatively for a real example in the results section. In addition, finite element analysis is carried out for comparison.

• Coupled systems mechanics
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• 제3권4호
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• pp.385-403
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• 2014

In this paper, the forced vibration problem of an Euler-Bernoulli beam that is joined with a semi-infinite field of a compressible fluid is considered as a boundary value problem (BVP). This BVP includes two partial differential equations (PDE) and some boundary conditions (BC), which are introduced comprehensively. After that, the closed-form solution of this fluid-structure interaction problem is obtained in the frequency domain. Some mathematical techniques are utilized, and two unknown functions of the BVP, including the beam displacement at each section and the fluid dynamic pressure at all points, are attained. These functions are expressed as an infinite series and evaluated quantitatively for a real example in the results section. In addition, finite element analysis is carried out for comparison.

• 대한수학회보
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• 제39권4호
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• pp.589-606
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• 2002

We introduce and analyze a frequency-domain method for parabolic partial differential equations. The method is naturally parallelizable. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we propose to solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution in the space-time domain. Existence and uniqueness as well as error estimates are given. Fourier invertibility is also examined. Numerical experiments are presented.