• 대한수학회지
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• 제52권6호
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• pp.1149-1159
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• 2015

This paper is concerned with a generalized 2D parabolic equation with a nonautonomous perturbation $$-{\Delta}u_t+{\alpha}^2{\Delta}^2u_t+{\mu}{\Delta}^2u+{\bigtriangledown}{\cdot}{\vec{F}}(u)+B(u,u)={\epsilon}g(x,t)$$. Under some proper assumptions on the external force term g, the upper semicontinuity of pullback attractors is proved. More precisely, it is shown that the pullback attractor $\{A_{\epsilon}(t)\}_{t{\epsilon}{\mathbb{R}}}$ of the equation with ${\epsilon}>0$ converges to the global attractor A of the equation with ${\epsilon}=0$.

• 한국음향학회지
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• 제33권6호
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• pp.383-391
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• 2014

수중의 음향 신호를 탐지하기 위하여 다양한 배열 형태를 가지는 소나가 개발되어 왔으며, 그 중 하나로 견인선배열 소나가 널리 사용된다. 견인 선배열 소나는 매우 긴 형태의 배열을 사용하므로, 회전에 의한 형상 왜곡에 의해 성능이 저하되는 단점이 있다. 이를 해결하기 위하여 회전하는 견인 선배열 소나에 대한 포물선 형태의 형상 모델을 이용하는 기법이 고안되었다. 본 논문에서는 포물선 모델을 이용하여 간섭 신호를 제거하는 적응 빔 형성기 설계 기법을 제안한다. 고안된 빔형성기 시스템은 일반화된 부엽 제거기 구조와 자가 조율 시스템에 기반을 두어 개발되었다.

• Steel and Composite Structures
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• 제35권5호
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• pp.671-685
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• 2020

This manuscript presents impacts of gradation of material functions and axial load functions on critical buckling loads and mode shapes of functionally graded (FG) thin and thick beams by using higher order shear deformation theory, for the first time. Volume fractions of metal and ceramic materials are assumed to be distributed through a beam thickness by both sigmoid law and symmetric power functions. Ceramic-metal-ceramic (CMC) and metal-ceramic-metal (MCM) symmetric distributions are proposed relative to mid-plane of the beam structure. The axial compressive load is depicted by constant, linear, and parabolic continuous functions through the axial direction. The equilibrium governing equations are derived by using Hamilton's principles. Numerical differential quadrature method (DQM) is developed to discretize the spatial domain and covert the governing variable coefficients differential equations and boundary conditions to system of algebraic equations. Algebraic equations are formed as a generalized matrix eigenvalue problem, that will be solved to get eigenvalues (buckling loads) and eigenvectors (mode shapes). The proposed model is verified with respectable published work. Numerical results depict influences of gradation function, gradation parameter, axial load function, slenderness ratio and boundary conditions on critical buckling loads and mode-shapes of FG beam structure. It is found that gradation types have different effects on the critical buckling. The proposed model can be effective in analysis and design of structure beam element subject to distributed axial compressive load, such as, spacecraft, nuclear structure, and naval structure.