• Tribology and Lubricants
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• v.30 no.1
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• pp.15-20
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• 2014

A more accurate expression for effective viscosity is obtained using a linear regression of the data from Fukui-Kaneko's model, which are obtained through numerical calculations based on the linearized Boltzmann equation. Veijola and Turowski's expression is adopted as a base function for effective viscosity. The four coefficients in that equation are optimized, and sensitivity analysis is conducted for these coefficients. The results show that the coefficient for the first-order Knudsen number is the most accurate, whereas the coefficient in the exponential of the Knudsen number is the least accurate compared with Fukui-Kaneko's results. The expression for effective viscosity is accurate within 0.02% rms of Fukui-Kaneko's results for the inverse Knudsen numbers from 0.01 to 100 and surface accommodation coefficients ranging from 0.7 to 1.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.11
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• pp.1907-1916
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• 2003

During decades, there has been much progress in understanding of the inelastic behavior of the materials and numerous inelastic constitutive equations have been developed. The complexity of these constitutive equations generally requires a stable and accurate numerical method. To obtain the increment of state variable, its evolution laws are linearized by several approximation methods, such as general midpoint rule(GMR) or general trapezoidal rule(GTR). In this investigation, semi-implicit integration schemes using GTR and GMR were developed and implemented into ABAQUS by means of UMAT subroutine. The comparison of integration schemes was conducted on the simple tension case, and simple shear case and nonproportional loading case. The fully implicit integration(FI) was the most stable but amplified the truncation error when the nonlinearity of state variable is strong. The semi-implicit integration using GTR gave the most accurate results at tension and shear problem. The numerical solutions with refined time increment were always placed between results of GTR and those of FI. GTR integration with adjusting midpoint parameter can be recommended as the best integration method for viscoplastic equation considering nonlinear kinematic hardening.

• Water for future
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• v.18 no.1
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• pp.85-94
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• 1985

A method is developed for the separation of the major base flow in a river hydrograph combining the numerical techniques and the empirical methods. The linearized Boussinesq equation and the storage function are used to obtain the base flow recession. The shape of base flow curve made by the recharge of the groundwater table aquifer resulting from rainfall in determined by the Singh and Stall's graphical method, and the continuous from for the curve is approximated by the multiple and polynomial regression. this procedure was successfully tested for the separation of base flow and the establishment of hydrograph in a natural watershed. It was found that the direct numerical method applied to the homogeneous linear second order ordinary differential equation system is not suited to obtain the recession curve, and the case that the loss is generated in the partially penetrating stream can not be solved by the method of this study.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.9
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• pp.1376-1385
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• 1993

This paper presents a new dynamic model which is represented by the second order differenatial equation and itcludes the robot arm dynamics as well as the actuator dynamics. The model exhibits excellent performance in the steady state and transient response. In addition the time varing nonlinear and coupled dynamic system has been linearized and decoupled by using nonlinear feedback and linearization method. In this case a pole assignment law is used to improve stability, and the optimal control altorithm is applied to the error equation to minimize the path error. In applying the proposed algorithm to the three joint manipulator with actuators, we obtained very encouraging results.

• Structural Engineering and Mechanics
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• v.56 no.3
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• pp.491-506
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• 2015

Propagation of the generalized Rayleigh waves in an initially stressed elastic half-space covered by an elastic layer is investigated. It is assumed that the initial stresses are caused by the uniformly distributed normal compressional forces acting on the face surface of the covering layer. Two different cases where the compressional forces are "dead" and "follower" forces are considered. Three-dimensional linearized theory of elastic waves in initially stressed bodies in plane-strain state is employed and the elasticity relations of the materials of the constituents are described through the Murnaghan potential where the influence of the third order elastic constants is taken into consideration. The dispersion equation is derived and an algorithm is developed for numerical solution to this equation. Numerical results for the dispersion of the generalized Rayleigh waves on the influence of the initial stresses and on the influence of the character of the external compressional forces are presented and discussed. These investigations provide some theoretical foundations for study of the near-surface waves propagating in layered mechanical systems with a liquid upper layer, study of the structure of the soil of the bottom of the oceans or of the seas and study of the behavior of seismic surface waves propagating under the bottom of the oceans.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.1
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• pp.1-14
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• 1998

A two-dimensional numerical model for tidal currents based on the depth averaged equation is developed. The mode1 employs a rectangular grid system for its simplicity in the application of complicate coastal shore lines. To raise computing efficiency, implicit approximate factorization scheme is implemented in solving governing equations. An upwind-differencing is used to discretize convective terms, which provides a numerical dissipation automatically and suppresses any oscillations caused by nonlinear instabilities. Some numerical tests are made against the analytic solutions of a linearized shallow water equation to validate the developed numerical scheme, and comparisons of the model prediction with the analytic solution are satisfactory. As a real application, the tidal currents are computed on the Inchon area where the tidal currents are important for the design of new canal which is under construction.

• Coupled systems mechanics
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• v.10 no.2
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• pp.123-142
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• 2021

The paper deals with the study of the dispersion of quasi-Lamb waves in a hydro-elastic system consisting of an elastic plate, barotropic compressible inviscid fluid, and rigid wall. The motion of the plate is described using the exact equations of elastodynamics, however, the flow of the fluid using the linearized equations and relations of the Navier-Stokes equations. The corresponding dispersion equation is obtained and this equation is solved numerically, as a result of which the corresponding dispersion curves are constructed. The main attention is focused on the effect of the presence of the fluid and the effect of the fluid layer thickness (i.e., the fluid depth) on the dispersion curves. The influence of the problem parameters on the dispersion curves related to the quasi-Scholte wave is also considered. As a result of the analyses of the numerical results, concrete conclusions are made about the influence of the fluid depth, the rigid wall restriction on the fluid motion, and the material properties of the constituents on the dispersion curves. During the analyses, the zeroth and the first four modes of the propagating waves are considered.

• Structural Engineering and Mechanics
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• v.81 no.4
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• pp.443-459
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• 2022

The paper studies the dispersion and attenuation of propagating waves in the "plate+compressible viscous fluid layer" system in the case where the fluid layer flow is restricted with a rigid wall, and in the case where the fluid layer has a free face. The motion of the plate is described by the exact equations of elastodynamics and the flow of the fluid by the linearized Navier-Stokes equations for compressible barotropic Newtonian viscous fluids. Analytical expressions are obtained for the amplitudes of the sought values, and the dispersion equation is derived using the corresponding boundary and compatibility conditions. To find the complex roots of the dispersion equation, an algorithm based on equating the modulus of the dispersion determinant to zero is developed. Numerical results on the dispersion and attenuation curves for various pairs of plate and fluid materials under different fluid layer face conditions are presented and discussed. Corresponding conclusions on the influence of the problem parameters on the dispersion and attenuation curves are made and, in particular, it is established that the change of the free face boundary condition with the impermeability condition can influence the dispersion and attenuation curves not only in the quantitative, but also in the qualitative sense.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.833-847
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• 2021

The horizontal porous baffle and its effect as an anti-slosh device have been investigated intensively in a swaying and rolling rectangular tank. To accurately assess the level at which porous baffles reduce liquid sloshing, the Matched Eigenfunction Expansion Method (MEEM) has been utilized as an analytical tool. The velocity potentials in the horizontal baffle-covered fluid region are expressed by the sum of the homogeneous and particular solutions to avoid solving the complex dispersion equation. By applying an equivalent linearized quadratic loss model, the nonlinear algebraic equation is derived and solved by implementing the Newton-Raphson iterative scheme. To prove the validity of the present theoretical model, a series of experiments have been conducted with different centered horizontal porous baffles with varying porosities and submerged depths in a swaying and rolling rectangular tank. Reasonably good agreements are obtained regarding the analytical solutions and the experiment's findings. The influence of porosity, submerged depth, and length of a centered horizontal porous baffle on anti-slosh performance have been analyzed, especially at resonance modes. The developed predictive tool can potentially provide guidelines for optimal design of the horizontal porous baffle.

• Journal of Astronomy and Space Sciences
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• v.24 no.4
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• pp.315-326
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• 2007

Recently introduced, several explicit solutions of relative motion between neighboring elliptic satellite orbits are reviewed. The performance of these solutions is compared with an analytic solution of the general linearized equation of motion. The inversion solution by the Hill-Clohessy-Wiltshire equations is used to produce the initial condition of numerical results. Despite the difference of the reference orbit, the relative motion with the relatively small eccentricity shows the similar results on elliptic case and circular case. In case of the 'chief' satellite with the relatively large eccentricity, HCW equation with the circular reference orbit has relatively larger error than other elliptic equation of motion does.