• Steel and Composite Structures
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• v.51 no.4
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• pp.457-471
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• 2024

In this research, for the first time the instability boundaries for a spinning shaft reinforced with graphene nanoplatelets undergone the principle parametric resonance are determined and examined taking into account the gyroscopic effect. In this respect, the extracted equations of motion in our previous research (Ref. Asadi et al. (2023)) are implemented and efficiently upgraded. In the upgraded discretized equations the effect of the Rayleigh's damping and the varying spinning speed is included that leads to a different dynamical discretized governing equations. The previous research was about the free vibration analysis of spinning graphene-based shafts examined by an eigen-value problem analysis; while, in the current research an advanced mechanical analysis is addressed in details for the first time that is the dynamics instability of the aforementioned shaft subjected to the principal parametric resonance. The spinning speed of the shaft is considered to be varied harmonically as a function of time. Rayleigh's damping effect is applied to the governing equations in order to regard the energy loss of the system. Resorting to Bolotin's route, Floquet theory and β-Newmark method, the instability region and its accompanied boundaries are defined. Accordingly, the effects of the graphene nanoplatelet on the instability region are elucidated.

• Journal of Mechanical Science and Technology
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• v.20 no.9
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• pp.1323-1338
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• 2006

An analytical method to estimate the coupled frequencies of the circular plate submerged in fluid is developed using the finite Fourier-Bessel series expansion and Rayleigh-Ritz method. To verify the validity of the analytical method developed, finite element method is used and the frequency comparisons between them are found to be in good agreement. For the perforated plate submerged in fluid, it is almost impossible to develop a finite element model due to the necessity of the fine meshing of the plate and the fluid at the same time. This necessitates the use of solid plate with equivalent material properties. Unfortunately the effective elastic constants suggested by the ASME code are found to be not valid for the modal analysis. Therefore in this study the equivalent material properties of perforated plate are suggested by performing several finite element analyses with respect to the ligament efficiencies.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.7 s.262
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• pp.620-627
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• 2007

In this paper, we adapt a modified internal energy non-equilibrium first-order extrapolation thermal boundary condition to the thermal lattice Boltzmann model (TLBM). This model is the double populations approach to simulate hydrodynamic and thermal fields. The bounce-back boundary condition which is a traditional boundary condition of lattice Boltzmann method has only a first order in numerical accuracy at the boundary and numerical instability. A non-equilibrium first-order extrapolation boundary condition has been verified to be of better numerical stability than the bounce-back boundary condition and this boundary condition is proved to be of second-order accuracy for the flat boundaries. The two-dimensional natural convection flow in a square cavity with Pr=0.71 and various Rayleigh numbers are simulated. The results are found to be in good agreement with those of previous studies.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.721-724
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• 2005

With the advantages of large vibration energy dissipation of structures, the granular materials are used as vibration and acoustic treatments. In this case of vibro acoustic controls, a finite dynamic strength of the solid component (frame) is an important design factor. The dynamic stiffness of hollow cylindrical beams containing porous and granular materials as damping treatment was measured. Using the Rayleigh-Ritz method, the effects of damping materials on the dynamic characteristics of beams were investigated. The results suggested that the acoustic structure Interaction between the frame and the structure enhances the dissipation of the vibration energy significantly. The same methods were applied also to vibration control of sandwich panels. By filling the cavities of honeycomb cores using unconsolidated granular materials, its sound transmission toss was improved significantly.

• Proceedings of the Korea Concrete Institute Conference
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• 2002.05a
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• pp.303-308
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• 2002

A governing differential equation (GDE) of PSC flexural member with constant eccentricity considering the long-term losses including concrete creep, shrinkage, and PS steel relaxation is derived based on the two approaches. The first approach utilizes the force and moment equilibrium equations derived based on the geometry of strains of the uniform and curvature strains while the second one utilizes the principle of minimum total potential energy formulation. The identity of the two GDE's is verified by comparing the coefficients consisting of the GDE's. The boundary conditions resulting from the functional analysis of the variational calculus are investigated. Rayleigh-Ritz method provides a way to get the explicit form of the continuous deflection function in which the total potential energy is minimized with respect to the unknown coefficients consisting of the trial functions. As a closure, the analytically calculated results are compared with the experiments and show good agreements.

• Solar Energy
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• v.8 no.2
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• pp.66-72
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• 1988

Natural convection in a horizontal annulus with spacers has been studied on the effects of diameter ratio and Rayleigh numbers and position of spacers by experimental method. In case of vertical spacers, the local spacer Nusselt numbers show positive values on the lower spacer, but negative values on the upper spacer. In case of horizontal spacers, the local spacer Nusselt numbers show positive values on the upward surface of spacer, but negative values on the downward surface of spacer. The mean tube Nusselt numbers and mean cylinder Nusselt numbers with vertical spacer are increased 10% and 2.1%, respectively by those of horizontal spacer.

• Solar Energy
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• v.13 no.1
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• pp.31-38
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• 1993

A numerical study of natural convection heat transfer confined by circular parallel walls at different temperatures and flat adiabatic walls is investigated for Rayleigh numbers from $10^3$ to $10^5$and sectorial angles from $30^{\circ}$ to $180^{\circ}$. It is used by a finite difference method to solve the governing equations. The results show velocity and temperature distributions. Mean Nusselt numbers are shown by $\overline{Nu}=C(Ra_L)^m$.

• Solar Energy
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• v.5 no.2
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• pp.3-10
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• 1985

This paper is concerned with the characterized method of wind speed distribution for calculation of wind power density of regional group and wind potential in Korea. It is shown that the Rayleigh distribution, K = 2, is not suitable for analyzing wind data in Korea. Simple relationship, K = 0.21 V + 0.84, is derived from Weibull wind distribution by analyzing wind data obtained from 24 meteorological station and is a suitable tool for estimation of wind power density. Application of this result, the domestic ideal and actual wind potential are estimated as $3.16{\times}10^9$ KWH/year and $7.14{\times}$10^8 KWH/year respectively for the case of 10 meter height, $1m^2$ swept area and $0.1{\times}0.1Km^2$ land area. And for the case of 50 meter height, ideal and actual wind potential are increased as $7.56{\times}10^9$ KWH/year and $2.37{\times}10^9$ KWH/year respectively.

• Solar Energy
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• v.6 no.2
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• pp.62-69
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• 1986

An analysis is made of the fully developed laminar flow and heat transfer in a parallel flat plate with heated rectangular block arrays to investigated the influence of bouyancy force. The shrouds is considered as adiabatic, while the heated block surface transmit a uniform rate of heat flux per unit axial length. The governing equations for velocity and temperature are solved by SIMPLE(Semi-Implicit Method Pressure Linked Equation) algorithm. Detailed velocity and temperature fields and overall heat transfer on wide range of Rayleigh number and various aspect ratios of heated rectangular blocks are computed. The result show that bouyancy leads to a significient enhancement in heat transfer along with a smaller increase in pressure drop, with the great enhancement found when the aspect ratio is 3.0.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.2
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• pp.72-77
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• 2002

In this paper, a simple method to measure the residual stress in microstructure is presented. In order to find the residual stress in micro-machined beam, the first natural frequency of the beam that has the residual stress inside is analyzed using Rayleigh's energy method. Micro gold electroplated structure is fabricated by surface micro-machining process including electroplating. The made structure is an approximate shape of clamped-clamped beam and its 1 st natural frequency is measured by resonance method. For the better estimation of the residual stress, an equivalent length of micro-fabricated beam to ideal beam is calculated by FEM. The residual stress was estimated from the equivalent length and the measured natural frequency. It was found that a tensile stress was residue in the micro beam structure.