• Structural Engineering and Mechanics
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• v.91 no.2
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• pp.197-209
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• 2024

The vibration of elastically supported bidirectional functionally graded (BDFG) sandwich beams on an elastic foundation is investigated. The sandwich structure is composed of upper and lower layers of BDFG material and the core layer of isotropic material. Material properties of upper and lower layers are assumed to vary continuously along the length and thickness of the beam with a power-law function. Hamilton's principle is used to deduce the vibration equations of motion of the sandwich Timoshenko beam. Then, the partial differential equation of motion is spatially discretized into a time-varying ordinary differential equation in terms of Chebyshev differential matrices. The eigenvalue equation associated with the free vibration is formulated to study the influence of various slenderness ratios, material gradient indexes, thickness ratios, foundation and support spring constants on the vibration frequency of BDFG sandwich beams. The present method can provide researchers with deep insight into the impact of various geometric, material, foundation and support parameters on the vibration behavior of BDFG sandwich beam structures.

• Journal of Advanced Marine Engineering and Technology
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• v.19 no.2
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• pp.27-35
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• 1995

액체 상태인 Pb-Sn 합금에 의한 이중확산유동에 대해 체비세프 콜로케이션 기법을 이용하여 수치해석하였다. 온도차에 의한 부력과 농도차에 의한 부력이 작을때에는 유동형태가 서서히 준정상상태에 이르러 아무런 진동현상을 볼 수 없다. 부력이 증가함에 따라 유동은 수직 농도 경계층을 파괴하여 플륨(Plume)형태의 유동을 생성시키고, 이는 시스템 내부로 성장한 후 소멸된다. 이러한 현상이 반복되면서 높은 주파수의 진동현상을 관찰할 수 있다.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.282-289
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• 2000

Direct numerical solution for flow and heat transfer for Benard convection with a body is obtained using an accurate and efficient Fourier-Chebyshev collocation and multi-domain method. The flow and temperature fields are obtained fur different Rayleigh numbers and thermal boundary conditions of body. The body has adiabatic and constant temperature conditions. The existence of a body gives different flow and heat transfer fields in the system, compared to pure Benard convection. The flow and temperature fields are also affected by the thermal boundary condition of a body.

• Proceedings of the KIEE Conference
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• 2008.10c
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• pp.83-85
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• 2008

본 논문은 변압기의 대부분 고장원인이 되는 권선 간의 단자 시 발생하는 진동을 수치적으로 계산하고 전자력 계산을 위한 방법으로 Pseudospectral Method을 적용하여 단락권선사이의 강제진동해석을 수행하였다. 나선형권선의 방정식은 Chebyshev다항식 시리즈의 확장과 Gauss-Lobatto collocation 과정을 수행되어진다. 알고리즘 검증을 위하여 22.9kV/220V, 1000kVA 용량의 케이블 타입의 변압기의 FEM 시물레이션 결과와 이론적 수치적계산과 함께 비교하였다.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.12 s.243
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• pp.1344-1351
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• 2005

Three-dimensional, time-dependent solutions of fluid flow past a circular cylinder with a periodic array of circular fins are obtained using an accurate and efficient spectral multidomain methodology. A Fourier expansion with a corresponding uniform grid is used along the circumferential direction. A spectral multidomain method with Chebyshev collocation is used along the r-z plane to handle the periodic array of circular fins attached to the surface of the cylinder. Unlike the flow past a circular cylinder, Second instabilities like mode A and mode B are not found in the Reynolds number range $100\~500$. It is found that three-dimensional instability of vortical structures is suppressed due to the presence of fin. The present numerical solutions report the detailed information of flow quantities near wake of finned cylinder.

• Journal of Magnetics
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• v.21 no.3
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• pp.468-475
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• 2016

In this article, entropy generation on MHD Williamson nanofluid over a porous shrinking sheet has been analyzed. Nonlinear thermal radiation and chemical reaction effects are also taken into account with the help of energy and concentration equation. The fluid is electrically conducting by an external applied magnetic field while the induced magnetic field is assumed to be negligible due to small magnetic Reynolds number. The governing equations are first converted into the dimensionless expression with the help of similarity transformation variables. The solution of the highly nonlinear coupled ordinary differential equation has been obtained with the combination of Successive linearization method (SLM) and Chebyshev spectral collocation method. Influence of all the emerging parameters on entropy profile, temperature profile and concentration profile are plotted and discussed. Nusselt number and Sherwood number are also computed and analyzed. It is observed that entropy profile increases for all the physical parameters. Moreover, it is found that when the fluid depicts non-Newtonian (Williamson fluid) behavior then it causes reduction in the velocity of fluid, however, non-Newtonian behavior enhances the temperature and nanoparticle concentration profile.

• International Journal of Naval Architecture and Ocean Engineering
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• v.4 no.1
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• pp.9-19
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• 2012

A set of equations of motion is derived for vibratory motions of an underwater cable connected to a moving vehicle at one end and with drogues at the other end. From the static analysis, cable configurations are obtained for different vehicle speeds and towing pretensions are determined by fluid resistance of drogues. Also the dynamic analysis is required to predict its vibratory motion. Nonlinear fluid drag forces greatly influence the dynamic tension. In this study, a numerical analysis program was developed to find out the characteristic of cable behaviour. The motion is described in terms of space and time coordinates based on Chebyshev polynomial expansions. For the spatial integration the collocation method is employed and the Newmark method is applied for the time integration. Dynamic tensions, displacements, velocities, accelerations were predicted in the time domain while natural frequencies and transfer functions were obtained in the frequency domain.

• Journal of the Society of Naval Architects of Korea
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• v.43 no.3 s.147
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• pp.285-293
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• 2006

Three-dimensional and time-dependent solution for the fluid flow and heat transfer past a circular cylinder with fins is obtained using accurate and efficient spectral methods. A Fourier expansion with a corresponding uniform grid is used along the circumferential direction. A spectral multi-domain method with a corresponding Chebyshev collocation is used along r-z plane to handle fins attached to the surface of a circular cylinder. At the Reynolds number of 300 based on a cylinder diameter, results with fins are compared with those without fins in order to see the effects of the presence of fins on three-dimensional and unsteady fluid flow and heat transfer past a bluff body. The detail structures of fluid flow and temperature field are obtained as a function of time to investigate how the presence of fins changes heat transfer mechanism related to the vortical structure in the wake region.