• Coupled systems mechanics
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• 제9권4호
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• pp.343-358
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• 2020

The present research deals with the time-harmonic deformation in transversely isotropic magneto thermoelastic solid with two temperature (2T), rotation due to inclined load and laser pulse. Generalized theory of thermoelasticity has been formulated for this mathematical model. The entire thermo-elastic medium is rotating with uniform angular velocity and subjected to thermally insulated and isothermal boundaries. The inclined load is supposed to be a linear combination of a normal load and a tangential load. The Fourier transform techniques have been used to find the solution to the problem. The displacement components, stress components, and conductive temperature distribution with the horizontal distance are computed in the transformed domain and further calculated in the physical domain using numerical inversion techniques. The effect of angle of inclination of normal and tangential load for Green Lindsay Model and time-harmonic source for Lord Shulman model is depicted graphically on the resulting quantities.

• Steel and Composite Structures
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• 제18권4호
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• pp.909-924
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• 2015

This paper investigates the vibration phenomenon of a nanobeam subjected to a time-dependent heat flux. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution law in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the functionally graded (FG) nanobeam is pure ceramic whereas the lower surface is pure metal. A nonlocal generalized thermoelasticity theory with dual-phase-lag (DPL) model is used to solve this problem. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and without energy dissipation can extracted as limited and special cases of the present model. An analytical technique based on Laplace transform is used to calculate the variation of deflection and temperature. The inverse of Laplace transforms are computed numerically using Fourier expansion techniques. The effects of the phase-lags (PLs), nonlocal parameter and the angular frequency of oscillation of the heat flux on the lateral vibration, the temperature, and the axial displacement of the nanobeam are studied.

• 한국구조물진단유지관리공학회 논문집
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• 제13권1호통권53호
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• pp.205-213
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• 2009

본 연구에서는 사장교의 케이블 장력을 장기적인 관점에서 보다 효과적으로 분석하고 모니터링할 수 있는 케이블 장력 모니터링 시스템을 개발하는 연구를 수행하였다. 제안된 모니터링 시스템에는 실시간 동적 데이터에서 일정 대상시간 동안의 가속도 데이터를 선정하고, 이를 고속 푸리에 변환 알고리즘에 적용하여 주파수 분석한 결과를 평균하여 일반화시키는 신호해석이론이 적용되었다. 제안된 케이블 장력의 모니터링 시스템의 적용성을 평가하기 위하여 실제 공용중인 사장교에 대한 현장재하시험을 실시하였다. 현장계측을 통한 수동으로 계산된 장력과 모니터링 시스템의 강제저장 기능을 통해 저장된 데이터를 수계산하여 반자동으로 계산된 장력을 비교한 결과, 장력차이가 1% 이내로 발생하였고, 제안된 모니터링 시스템에서 자동으로 계산된 장력을 비교한 결과에서는 약 5% 범위의 무시할만한 차이로 나타나 본 연구에서 제안된 사장교 케이블 장력 모니터링 시스템의 신뢰도를 검증하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권1호
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• pp.69-81
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• 2015

The present paper deals with the determination of temperature, displacement and thermal stresses in a semi-infinite hollow circular disk due to internal heat generation within it. Initially the disk is kept at arbitrary temperature F(r, z). For times t > 0 heat is generated within the circular disk at a rate of g(r, z, t) $Btu/hr.ft^3$. The heat flux is applied on the inner circular boundary (r = a) and the outer circular boundary (r = b). Also, the lower surface (z = 0) is kept at temperature $Q_3(r,t)$ and the upper surface ($Z={\infty}$) is kept at zero temperature. Hollow circular disk extends in the z-direction from z = 0 to infinity. The governing heat conduction equation has been solved by using finite Hankel transform and the generalized finite Fourier transform. As a special case mathematical model is constructed for different metallic disk have been considered. The results are obtained in series form in terms of Bessel's functions. These have been computed numerically and illustrated graphically.

• 한국통신학회논문지
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• 제24권8B호
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• pp.1558-1566
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• 1999

센서의 물리적인 한계에 의해서 저해상도의 영상밖에 얻을 수 없는 경우에도 고해상도의 영상이 필요할 때가 있다. 본 논문에서는 이러한 경우에 다중채널의 디컨벌루션 방법을 기반으로 다수의 저해상도 영상들로부터 하나의 고해상도 영상을 얻을 수 있는 영상 복원 알고리즘을 제안하고자 한다. 엘리어싱은 주파수 영역에서 해석하기 쉽기 때문에 DFT를 기반으로 한 방법이 일반적으로 사용되어졌다. 그러나 복원에 필요한 저해상도 영상이 충분하지 않거나, 저해상도 영상들이 가지는 정보가 적절하지 않을 경우에 대해서는 원하는 고해상도의 영상을 얻을 수 없었다. 그래서 이를 극복하기 위해 공간 영역으로 재해석하면 확장된 다중채널의 정규화를 사용할 수 있었으며, DFT대신에 DCT를 사용하여 연산량을 줄일 수 있었다. 이론적인 고찰과 실험을 통하여 우리가 제안한 알고리즘에 대한 유용성을 알아보았으며, 저해상도 영상의 움직임 정보가 올바르지 않을 경우에도 정규화를 사용하여 이를 극복할 수 있음을 실험을 통해서 알 수 있었다.

• 수산해양기술연구
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• 제35권4호
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• pp.435-447
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• 1999

It is main objective of this approach to present a method to analyse stochastic design sensitivity for problems of structural dynamics with randomness in design parameters. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element approach. An alternative form of the constant functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The terminal problem of the adjoint system is solved using equivalent homogeneous equations excited by initial velocities. The numerical procedures are shown to be much more efficient when based on the fold superposition method: the generalized co-ordinates are normalized and the correlated random variables are transformed to uncorrelated variables, whereas the secularities are eliminated by the fast Fourier transform of complex valued sequences. Numerical algorithms have been worked out and proved to be accurate and efficient : they can be readily adapted to fit into the existing finite element codes whose element derivative matrices can be explicitly generated. The numerical results of two cases -2 dimensional portal frame for the comparison with reference and 3-dimensional frame structure - for the deterministic sensitivity analysis are presented.

• Structural Engineering and Mechanics
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• 제68권2호
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• pp.215-226
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• 2018

In this article, the theory of fractional order two temperature generalized thermoelasticity is employed to study the wave propagation in a fiber reinforced anisotropic thermoelastic half space in the presence of moving internal heat source. The whole space is assumed to be under the influence of gravity. The surface of the half-space is subjected to an inclined load. Laplace and Fourier transform techniques are employed to solve the problem. Expressions for different field variables in the physical domain are derived by the application of numerical inversion technique. Physical fields are presented graphically to study the effects of gravity and heat source. Effects of time, reinforcement, fractional parameter and inclination of load have also been reported. Results of some earlier workers have been deduced from the present analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권3호
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• pp.117-131
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• 2021

The problem of generalized thermoelasticity of two-temperature for finite piezoelectric rod will be modified by applying three different types of heating applications namely, thermal shock, ramp-type heating and harmonically vary heating. The solutions will be derived with direct approach by the application of Laplace transform and the Caputo-Fabrizio fractional order derivative. The inverse Laplace transforms are numerically evaluated with the help of a method formulated on Fourier series expansion. The results obtained for the conductive temperature, the dynamical temperature, the displacement, the stress and the strain distributions have represented graphically using MATLAB.

• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.371-381
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• 2021

In this paper, we attempt to obtain sufficient conditions for the existence of tight wavelet frame sets in locally compact abelian groups. The condition is generated by modulating a collection of characteristic functions that correspond to a generalized shift-invariant system via the Fourier transform. We present two approaches (for stationary and non-stationary wavelets) to construct the scaling function for L²(G) and, using the scaling function, we construct an orthonormal wavelet basis for L²(G). We propose an open problem related to the extension principle for Riesz wavelets in locally compact abelian groups.

• 대한수학회보
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• 제53권5호
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• pp.1531-1548
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• 2016

Let C[0, t] denote the space of real-valued continuous functions on [0, t] and define a random vector $Z_n:C[0,t]{\rightarrow}\mathbb{R}^n$ by $Z_n(x)=(\int_{0}^{t_1}h(s)dx(s),{\ldots},\int_{0}^{t_n}h(s)dx(s))$, where 0 < $t_1$ < ${\cdots}$ < $ t_n=t$ is a partition of [0, t] and $h{\in}L_2[0,t]$ with $h{\neq}0$ a.e. Using a simple formula for a conditional expectation on C[0, t] with $Z_n$, we evaluate a generalized analytic conditional Wiener integral of the function $G_r(x)=F(x){\Psi}(\int_{0}^{t}v_1(s)dx(s),{\ldots},\int_{0}^{t}v_r(s)dx(s))$ for F in a Banach algebra and for ${\Psi}=f+{\phi}$ which need not be bounded or continuous, where $f{\in}L_p(\mathbb{R}^r)(1{\leq}p{\leq}{\infty})$, {$v_1,{\ldots},v_r$} is an orthonormal subset of $L_2[0,t]$ and ${\phi}$ is the Fourier transform of a measure of bounded variation over $\mathbb{R}^r$. Finally we establish various change of scale transformations for the generalized analytic conditional Wiener integrals of $G_r$ with the conditioning function $Z_n$.