• Advances in concrete construction
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• v.14 no.2
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• pp.103-113
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• 2022

On the basis of fabrication, the utilization of nano material in numerous industrial and technological system, obtained the utmost significance in current decade. Therefore, the current investigation presents a theoretical disposition regarding the flow of electric conducting Williamson nanoliquid over a stretchable surface in the presence of the motile microorganism. The impact of thermal radiation and magnetic parameter are incorporated in the energy equation. The concentration field is modified by adding the influence of chemical reaction. Moreover, the splendid features of nanofluid are displayed by utilizing the thermophoresis and Brownian motion aspects. Compatible similarity transformation is imposed on the equations governing the problem to derive the dimensionless ordinary differential equations. The Homotopy analysis method has been implemented to find the analytic solution of the obtained differential equations. The implications of specific parameters on profiles of velocity, temperature, concentration and motile microorganism density are investigated graphically. Moreover, coefficient of skin friction, Nusselt number, Sherwood number and density of motile number are clarified in tabular forms. It is revealed that thermal radiation, thermophoresis and Brownian motion parameters are very effective for improvement of heat transfer. The reported investigation can be used in improving the heat transfer appliances and systems of solar energy.

• Journal of Astronomy and Space Sciences
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• v.2 no.1
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• pp.19-33
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• 1985

The singularities of differential Newtonian equation of motion in three body problem cause the loss of accuracy and the considerable increase of the computer time. These singularities could be eliminated during the process of regularization to transform the independent variables and the coordinate of Newtonian equations of motion. In this study, we calculated the positions and velocities of three body along the time scale to find out the unique solution of regularized Newtonian equations of motion with the $5^{th}$ order Runge-Kutta method by assuming the suitable initial velocities and positions. As the results of these calculations it is shown that the tripe stellar system eventually distintegrated, two of them formed a binary, and the last one escaped from this system with a hyperbolic orbit. This may suggest one possible explanation for the binary formation.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.2
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• pp.38-47
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• 1992

The motion response of a ship moored in a rectangular harbor excited by long waves has been studied theoretically and experimentally. Within the framework of potential theory, matched asymptotic expansion techniques are exployed to analyze the problem. The fluid domain is divided into the ocean and the harbor regions for the analysis of wave response in a harbor without ship. The wave responses in both the ocean and the harbor sides are solved first independently in terms of Green's functions, which are the solutions of the Helmholtz equation satisfying appropriate boundary conditions. Slender body approximations are used to obtain the velocity jumps across the ship, which are associated with the symmetric motion modes of the ship. Unknowns contained in each solution are finally determined by matching at an intermediate zone between two neighboring regions. Theoretical results predict the ship motion qualitatively well. The main source of quantitative discrepancies is presumably due to real fluid effects such as separation at the harbor entrance and friction on harbor boundaries.

• Structural Engineering and Mechanics
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• v.90 no.6
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• pp.551-568
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• 2024

The present study deals with static and dynamic behaviors including forced vibrations of an elastic rectangular nano plate on the two-parameter foundation. Firstly, the rectangular plate is assumed to be subjected to uniformly distributed and eccentrically applied concentrated loads. The governing equations of the problem are derived by considering the dynamic response of the plate, employing a series of the Chebyshev polynomials for the displacement function and applying the Galerkin method. Then, effects of the non-essential boundary conditions of the plate, i.e., the boundary conditions related to the shearing forces, the bending moments and the corner forces, are included in the governing equation of motion to compensate for the non-satisfied boundary conditions and increase the accuracy of the Galerkin method. The approximate numerical solution is accomplished using an iterative process due to the non-linearity of the unilateral property of the two-parameter foundation. The plate under static concentrated load is investigated in detail numerically by considering a wide range of parameters of the plate and the foundation stiffnesses. Numerical treatment of the problem in the time domain is carried out by assuming a stepwise variation of the concentrated load and the linear acceleration procedure is employed in the solution of the system of governing differential equations derived from the equation of motion. Time variations of the contact region and those of the displacements of the plate are presented in the figures for various numbers of the two-parameter of the foundation, as well as the classical and nano parameters of the plate particularly focusing on the non-linearity of the problem due to the plate lift-off from the unilateral foundation. The effects of classical and nonlocal parameters and loading are investigated in detail. Definition of the separation between the plate and the two-parameter foundation is presented and applied to the given problem. The effect of the lift-off on the static and dynamic behavior of the rectangular plate is studied in detail by considering various loading conditions. The numerical study shows that the effect of nonlocal parameters on the behavior of the plate becomes significant, when nonlinearity becomes more profound, due to the lift-off of the plate. It is seen that the size effects are significant in static and dynamic analysis of nano-scaled rectangular plates and need to be included in the mechanical analyses. Furthermore, the corner displacement of the plate is affected more significantly from the lift-off, whereas it is less marked in the time variation of the middle displacement of the plate. Several numerical examples are presented to examine the sensibility of various parameters associated with nonlocal parameters of the plate and foundation. Both stiffening and softening nonlocal parameters behavior of the plate are identified in the numerical solutions which show that increasing the foundation stiffness decreases the extent of the contact region, whereas the stiffness of the shear layer increases the contact region and reduces the foundation settlement considerably.

• Journal of the Korean Geotechnical Society
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• v.19 no.4
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• pp.133-144
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• 2003

The resonant column testing is a laboratory testing method to determine the shear modulus and material damping factor of soils. The method has been widely used for many applications and its importance has increased. Since the first use of the testing method in 1960's, the low-technology electronic devices fir testing and data acquisition have limited the measurement only to the amplitude of the linear spectrum. The limitations of the testing method are also attributed to the assumption of linear-elastic material in the theory of the resonant column testing and also to the incomplete understanding of the dynamic behaviour of the resonant column testing device. Recently, Joh et al. proposed a theory to overcome the limitations of the resonant column testing by deriving the equation of motion and providing its solution for the resonant column testing device. This study proposed the improved data reduction and analysis method for the resonant column testing, thanks to the advanced data acquisition system and the new theoretical solution for the resonant column testing system. For the verification of the proposed data reduction and analysis method, the numerical simulation of the resonant column testing was performed by the finite element analysis. Also, a series of resonant column testing were performed fir Joomunjin sand, which verified the feasibility of the proposed method and revealed the limitations of the conventional data reduction and analysis method.

• Geomechanics and Engineering
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• v.6 no.6
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• pp.517-530
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• 2014

Seismic ground response analysis is one of the most important issues in geotechnical earthquake engineering. Conventional seismic site response and free field analysis of layered soils does not consider the effect of surcharge mass which may be present on the top layer. Surcharge mass may develop extra inertial force to the soil and, hence, significantly affect on the results of seismic ground response analysis. Methods of analysis of ground response may also be categorized into time domain and frequency domain concepts. Simplicity in developing analytical relations and accuracy in considering soil dynamic properties dependency to loading frequency are benefits of frequency domain analysis. In this part of the paper, seismic ground response is analyzed using transfer function method for soil layers considering surcharge mass on the top layer. Equation of motion, wave equation, is solved using amended boundary conditions which effectively take the impact of surcharge mass into account. A computer program is developed by MATLAB software based on the solution method developed for wave equation. Layered soils subjected to earthquake loading were numerically studied and solved especially by the computer program developed in this research. Results obtained were compared with those given by DEEP SOIL computer program. Such comparison showed the accuracy of the program developed in this study. Also in this part, the effects of geometrical and mechanical properties of soil layers and especially the impact of surcharge mass on transfer function are investigated using the current approach and the program developed. The efficiency and accuracy of the method developed here is shown through some worked examples and through comparison of the results obtained here with those given by other approaches. Discussions on the results obtained are presented throughout in this part.

• Journal of Digital Contents Society
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• v.16 no.6
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• pp.909-916
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• 2015

This paper presents a method to display the 3D vector fields by analyzing phase space. This method is based on the connections between ordinary differential equations and the topology of vector fields. The phase space analysis should be geometric interpolation of an autonomous system of equation in the form of the phase space. Every solution of it system of equations corresponds not to a curve in a space, but the motion of a point along the curve. This analysis is the basis of this paper. This new method is required to decompose the hexahedral cell into five or six tetrahedral cells for 3D vector fields. The critical points can be easily found by solving a simple linear system for each tetrahedron. The tangent curves can be integrated by finding the intersection points of an integral curve traced out by the general solution of each tetrahedron and plane containing a face of the tetrahedron.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.40 no.5
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• pp.469-481
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• 2016

In this paper, a mathematical methodology was theoretically studied to obtain the impact force caused by the collision between rigid bodies. This theoretical methodology was applied to compute the impact force applied on the spent nuclear fuel disposal canister that accidentally drops and collides onto the ground. From this study, the impact force required to ensure a structurally safe canister design was theoretically formulated. The main content of the theoretical study concerns the rigid body kinematics and equation of motion during collision between two rigid bodies. On the basis of this study, a general impact theory to compute the impact force caused by the collision between two bodies was developed. This general impact theory was applied to theoretically formulate the approximate mathematical solution of the impact force that affects the spent nuclear fuel disposal canister that accidentally falls to the ground. Simultaneously, a numerical analysis was performed using the computer code to compute the numerical solution of the impact force, and the numerical result was compared with the approximate mathematical solution.

• Journal of the Society of Naval Architects of Korea
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• v.55 no.4
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• pp.297-305
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• 2018

In a shipyard, block lifting is an important process in the production of ships and offshore structures. Block lifting is a sensitive process because lifting blocks have to be erected with exact positions and orientations. If we use a numerical method for the process, it is important to find tensions of wires and positions of equalizers to maintain the initial equilibrium position of the block. At this time, equations of motion of the block should be solved to calculate the initial equilibrium position of the block. Because the solving technique changes according to the number of equalizers, a suitable equation for the corresponding problem is required. In this study, three types of equations are proposed to find the initial equilibrium position of the block according to the number of equalizers. The Newton-Raphson's method is used to solve nonlinear simultaneous equations and the optimization method is used to determine the appropriate solution to the undetermined problem. To evaluate the applicability of the proposed methods, the dynamic simulations are performed using the tensions calculated from the proposed methods, and the results are discussed. The results show that the proposed methods can be effectively used to determine initial equilibrium position of the block for the block lifting.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.3
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• pp.291-305
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• 2010

A three-dimensional time-domain calculation method is of crucial importance in prediction of the motions and wave loads of a ship advancing in a severe irregular sea. The exact solution of the free surface wave-ship interaction problem is very complicated because of the essentially nonlinear boundary conditions. In this paper, an approximate body nonlinear approach based on the three-dimensional time-domain forward-speed free-surface Green function has been presented. The Froude-Krylov force and the hydrostatic restoring force are calculated over the instantaneous wetted surface of the ship while the forces due to the radiation and scattering potentials over the mean wetted surface. The time-domain radiation and scattering potentials have been obtained from a time invariant kernel of integral equations for the potentials which are discretized according to the second-order boundary element method (Hong and Hong 2008). The diffraction impulse-response functions of the Wigley seakeeping model advancing in transient head waves at various Froude numbers have been presented. A simulation of coupled heave-pitch motion of a long rectangular barge advancing in regular head waves of large amplitude has been carried out. Comparisons between the linear and the approximate body nonlinear numerical results of motions and wave loads of the barge at a nonzero Froude number have been made.