• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.7 no.3
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• pp.528-537
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• 1995

Natural convective flow and heat transfer characteristics in a partially opened enclosure fitted with a horizontal divider are investigated numerically. The enclosure is composed of a lower hot and a upper cold horizontal walls and adiabatic vertical walls. A divider is attached perpendicularly to the vertical insulated wall. The governing equations are solved by using the finite element method with Galerkin method. The computations have been carried out by varying the length of divider, the opening size, and the Rayleigh number based on the temperature difference between two horizontal walls and the enclosure height for air(Pr=0.71). As result, when the opening size is fixed, the intensity of the secondary flow is weaken as the length of divider increases. The maximum heat transfer rate over the upper cold wall occurs at a position bounded on the opening. However, when the length of divider is increased considerably, its maximum occurs at the right wall. The stability and frequency of oscillation are affected by the Rayleigh number and length of divider. The Nusselt number is increased with the increase of the opening size and the increase of Rayleigh number.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.677-682
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• 2003

The non-linear dynamic characteristics of a semi-circular pipe conveying fluid are investigated when the pipe is clamped at both ends. To consider the geometric non-linearity for the radial and circumferential displacements, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived form the Galerkin method. The natural frequencies varying with the flow velocity are computed fen the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized- method. From these results, we should to describe the non-linear behavior to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.372-377
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• 2001

A new non-linear of a straight pipe conveying fluid is presented for vibration analysis when the pipe is fixed at both ends. Using the Euler-Bernoulli beam theory and the non-linear Lagrange strain theory, from the extended Hamilton's principle are derived the coupled non-linear equations of motion for the longitudinal and transverse displacements. These equations of motion for are discretized by using the Galerkin method. After the discretized equations are linearized in the neighbourhood of the equilibrium position, the natural frequencies are computed from the linearized equations. On the other hand, the time histories for the displacements are also obtained by applying the $generalized-{\alpha}$ time integration method to the non-linear discretized equations. The validity of the new modeling is provided by comparing results from the proposed non-linear equations with those from the equations proposed by $Pa{\ddot{i}}dousis$.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.12 no.2
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• pp.150-160
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• 2000

Turbulent natural convective flow and heat transfer in a square enclosure with horizontal partition are investigated numerically. The enclosure is composed of a lower hot and a upper cold horizontal walls and adiabatic vertical walls. Partitions carried with the upward, downward, and both control plates are attached perpendicularly to the one of the vertical insulated walls, respectively. The low Reynolds number $k-\varepsilon$ model is adopted to calculate the turbulent thermal convection. The governing equations are solved by using the finite element method with Galerkin method. The computations have been carried out by varying the length of partition, the position of control plates, and the Rayleigh number based on the temperature difference between two horizontal walls and the enclosure height for water(Pr=4.95). When the control plates are attached at the edge of partition, the stability of oscillating flow grows wrose with the increase of Rayleigh number and the partition length. The heat transfer rate has been reducer than that of no control plate due to the restraint of control plates with the increase of Rayleigh number.

• Journal of Korean Port Research
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• v.14 no.4
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• pp.451-461
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• 2000

The design and maintenance of navigation channel and water facilities of an harbor which is located at the mouth of river or at the estuary area are difficult due to the complexity of estuarial water and sediment circulation. Effects of deepening navigable waterways, of changing coastline configurations, or of discharging dredged material to the open sea are necessary to be investigated and predicted in terms of water quality and possible physical changes to the coastal environment. A borad analysis of the transport mechanism in the estuary area was made in terms of sediment property, falling velocity, concentration and flow characteristics. In order to simulate the transport processes, a two-dimensional finite element model is developed, which includes erosion, transport and deposition mechanism of suspended sediments. Galerkin’s weighted residual method is used to solve the transient convection-diffusion equation. The fluid domain is subdivided into a series of triangular elements in which a quadratic approximation is made for suspended sediment concentration. Model could deal with a continuous aggregation by stipulating the settling velocity of the flocs in each element. The model provides suspended sediment concentration, bed shear stress, erosion versus deposition rate and bed profile at the given time step.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.7 no.5
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• pp.793-800
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• 2006

DQM(differential quadrature method) is applied to computation of eigenvalues of the equations of motion governing the free in-plane vibration fur circular curved beams including both rotatory inertia and shear deformation. Fundamental frequencies are calculated for the members with clamped-clamped end conditions and various opening angles. The results are compared with numerical solutions by other methods for cases in which they are available. The differential quadrature method gives good accuracy even when only a limited number of grid points is used.

• Advances in nano research
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• v.8 no.1
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• pp.25-36
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• 2020

Rotating systems concern with torsional vibration, and it should be considered in vibration analysis. To do this, the time-dependent torsional vibrations in a single-walled carbon nanotube (SWCNT) under the linear and harmonic external torque, are investigated in this paper. Eringen's nonlocal elasticity theory is considered to demonstrate the nonlocality and constitutive relations. Hamilton's principle is established to derive the governing equation of motion and consequently related boundary conditions. An analytical method, called the Galerkin method, is utilized to discretize the driven differential equations. Linear and harmonic torsional loads, along with determined amplitude, are applied to the SWCNT as the external torques. SWCNT is considered under the clamped-clamped end supports. In free vibration, analysis of small scale effect reveals the capability of natural frequencies in different modes, and this results desirably are in coincidence with another study. The forced torsional vibration in the time domain, especially for carbon nanotubes, has not been done before in the previous works. The previous forced studies were devoted to the transverse vibrations. It should be emphasized that the dynamical analysis of torsion is novel, workable, and at the beginning of the path. The variations of nonlocal parameter, CNT's thickness, and the influence of excitation frequency on time-dependent angular displacement and nondimensional angular displacement are investigated in the context.

• Advances in materials Research
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• v.9 no.2
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• pp.115-131
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• 2020

Limit elastic speed analysis of Al/SiC-based functionally graded annular disk of uniform thickness has been carried out for two cases, namely: metal-rich and ceramic rich. In the present study, the unknown field variable for radial displacement is solved using variational method wherein the solution was obtained by Galerkin's error minimization principle. One of the objectives was to identify the variation of induced stress in a functionally graded disk of uniform thickness at limit elastic speed using modified rule of mixture by comparing the induced von-Mises stress with the yield stress along the disk radius, thereby locating the yield initiation. Furthermore, limit elastic speed has been reported for a combination of varying grading index (n) and aspect ratios (a/b).Results indicate, limit elastic speed increases with an increase in grading indices. In case of an increase in aspect ratio, limit elastic speed increases up to a critical value beyond which it recedes. Also, the objective was to look at the variation of yield stress corresponding to volume fraction variation within the disk which later helps in material tailoring. The study reveals the qualitative variation of yield stress for FG disk with volume fraction, resulting in the possibility of material tailoring from the processing standpoint, in practice.

• Structural Engineering and Mechanics
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• v.76 no.4
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• pp.451-463
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• 2020

In this paper, a new semi-analytical solution for estimating the pull-in parameters of electrically actuated functionally graded (FG) nanobeams is proposed. All the bulk and surface material properties of the FG nanoactuator vary continuously in thickness direction according to power law distribution. Here, the modified couple stress theory (MCST) and Gurtin-Murdoch surface elasticity theory (SET) are jointly employed to capture the size effects of the nanoscale beam in the context of Euler-Bernoulli beam theory. According to the MCST and SET and accounting for the mid-plane stretching, axial residual stress, electrostatic actuation, fringing field, and dispersion (Casimir or/and van der Waals) forces, the nonlinear nonclassical equation of motion and boundary conditions are obtained derived using Hamilton principle. The proposed semi-analytical solution is derived by employing Galerkin method in conjunction with the Particle Swarm Optimization (PSO) method. The proposed solution approach is validated with the available literature. The freestanding behavior of nanoactuators is also investigated. A parametric study is conducted to illustrate the effects of different material and geometrical parameters on the pull-in response of cantilever and doubly-clamped FG nanoactuators. This model and proposed solution are helpful especially in mechanical design of micro/nanoactuators made of FGMs.

• Smart Structures and Systems
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• v.10 no.1
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• pp.67-87
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• 2012

A dragonfly inspired flapping wing is investigated in this paper. The flapping wing is actuated from the root by a PZT-5H and PZN-7%PT single crystal unimorph in the piezofan configuration. The non-linear governing equations of motion of the smart flapping wing are obtained using the Hamilton's principle. These equations are then discretized using the Galerkin method and solved using the method of multiple scales. Dynamic characteristics of smart flapping wings having the same size as the actual wings of three different dragonfly species Aeshna Multicolor, Anax Parthenope Julius and Sympetrum Frequens are analyzed using numerical simulations. An unsteady aerodynamic model is used to obtain the aerodynamic forces. Finally, a comparative study of performances of three piezoelectrically actuated flapping wings is performed. The numerical results in this paper show that use of PZN-7%PT single crystal piezoceramic can lead to considerable amount of wing weight reduction and increase of lift and thrust force compared to PZT-5H material. It is also shown that dragonfly inspired smart flapping wings actuated by single crystal piezoceramic are a viable contender for insect scale flapping wing micro air vehicles.