• Journal of Ocean Engineering and Technology
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• v.19 no.1 s.62
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• pp.87-94
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• 2005

This paper investigates the constant-level luffing and time optimal control of jib cranes. The constant-level luffing, which is the sustainment of the load at a constant height during luffing, is achieved by analyzing the kinematic relationship between the angular displacement of a boom and that of the main hoist motor of a jib crane. Under the assumption that the main body of the crane does not rotate, the equations of motion of the boom are derived using Newton's Second Law. The dynamic equations for the crane system are highly nonlinear; therefore, they are linearized under the small angular motion of the load to apply linear control theory. This paper investigates the time optimal control from the perspective of no-sway at a target point. A stepped velocity pattern is used to design the moving path of the jib crane. Simulation results demonstrate the effectiveness of the time optimal control, in terms of anti-sway motion of the load, while luffing the crane.

• Smart Structures and Systems
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• v.22 no.3
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• pp.259-276
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• 2018

This paper studies the energies and energy release rate (ERR) for the initially rotationally symmetric compressed (or stretched) in the inward (outward) radial direction of the PZT/Elastic/PZT sandwich circular plate with interface penny-shaped cracks. The investigations are made by utilizing the so-called three-dimensional linearized field equations and relations of electro-elasticity for piezoelectric materials. The quantities related to the initial stress state are determined within the scope of the classical linear theory of piezoelectricity. Mathematical formulation of the corresponding problem and determination of the quantities related to the stress-strain state which appear as a result of the action of the uniformly normal additional opening forces acting on the penny-shaped crack's edges are made within the scope of the aforementioned three-dimensional linearized field equations solution which is obtained with the use of the FEM modelling. Numerical results of the energies and ERR and the influence of the problem parameters on these quantities are presented and discussed for the PZT- 5H/Al/PZT-5H, PZT-4/Al/PZT-4, $BaTiO_3/Al/BaTiO_3$ and PZT-5H/StPZT-5H sandwich plates. In particular, it is established that the magnitude of the influence of the piezoelectricity and initial loading on the ERR increases with crack radius length.

• Journal of the Society of Naval Architects of Korea
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• v.58 no.6
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• pp.348-357
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• 2021

In this paper, the generalized hydrodynamic force and response of a flexible body are calculated at different reference coordinate systems. We generalize the equation of motion for a flexible body by using the conservation of momentum (Mei et al., 2005). To obtain the equations in the generalized mode, two different reference coordinates are adopted. The first is the body-fixed coordinate system by a rigid body motion. The other is the inertial coordinate system which has been adopted for the analysis. Using the perturbation scheme in the weakly-nonlinear assumption, the equations of motion are expanded up to second-order quantities and several second-order forces are obtained. Numerical tests are conducted for the flexible barge model in head waves and the vertical bending is only considered in the hydroelastic responses. The results show that the linear response does not have the difference between the two formulations. On the other hand, second-order quantities have different values for which the rigid body motion is relatively large. However, the total summation of second-order quantities has not shown a large difference at each reference coordinate system.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.28 no.11
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• pp.434-443
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• 2016

The evaporation of water from an aqueous solution is widely used in the food, desalination, pulp, and chemical industries. Usually, a large amount of energy is consumed in the evaporation process to boil off water due to atmospheric pressure. As a way of improving the energy efficiency of the evaporation process, the combination of multiple effect evaporation and thermal vapor recompression has been proposed and has become a successful technique. In this study, 4 multiple-effect falling film type evaporators for sugar solution are designed and the energy efficiency of the system is analyzed in response to the selection of the steam ejector position. Energy efficiency is increased and vapor is more compressed in the steam ejector as the Thermal Vapor Recompression (TVR) is arranged in the rear part of the evaporator system. A simplified 0-dimensional evaporator model is developed using non-linear equations derived from mass balances, energy balances, and heat transfer equations. Steam economy is calculated to compare the evaporation performance of the 4 proposed evaporators. The entrainment ratio, compression ratio, and expansion ratio are computed to check the ejector performance.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.215-241
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• 2003

In this paper, solute transport in heterogeneous aquifers using a modified Fokker-Planck equation (MFPE) is investigated. This newly developed mathematical model is characterised with a time-, scale-dependent dispersivity. A two-dimensional finite volume quadrilateral mesh method (FVQMM) based on a quadrilateral background interpolation mesh is developed for analysing the model. The FVQMM transforms the coupled non-linear partial differential equations into a system of differential equations, which is solved using backward differentiation formulae of order one through five in order to advance the solution in time. Three examples are presented to demonstrate the model verification and utility. Henry's classic benchmark problem is used to show that the MFPE captures significant features of transport phenomena in heterogeneous porous media including enhanced transport of salt in the upper layer due to its parameters that represent the dependence of transport processes on scale and time. The time and scale effects are investigated. Numerical results are compared with published results on the some problems.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.371-399
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• 2006

The theoretical background and capabilities of the developed program, SAR-CWF, for stochastic analysis of 3D reinforced-concrete shear wall-frame structures subject to seismic excitations is presented. Incremental stiffness and strength properties of system members are modeled by extended Roufaiel-Meyer hysteretic relation for bending while shear deformations for walls by Origin-Oriented hysteretic model. For the critical height of shear-walls, division to sub-elements is performed. Different yield capacities with respect to positive and negative bending, finite extensions of plastic hinges and P-${\delta}$ effects are considered while strength deterioration is controlled by accumulated hysteretic energy. Simulated strong motions are obtained from a Gaussian white-noise filtered through Kanai-Tajimi filter. Dynamic equations of motion for the system are formed according to constitutive and compatibility relations and then inserted into equivalent It$\hat{o}$-Stratonovich stochastic differential equations. A system reduction scheme based on the series expansion of eigen-modes of the undamaged structure is implemented. Time histories of seismic response statistics are obtained by utilizing the computer programs developed for different types of structures.

• Journal for History of Mathematics
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• v.26 no.2_3
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• pp.149-161
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• 2013

The history of finding solutions of linear equations went back to some thousand years ago, and has been steadily developed to solve systems of higher degree polynomials. The method to eliminate variables came into use around the 17th and 18th century. This technique has been extended to the resultant theory that was laid in the 19th century by outstanding mathematicians as Euler, Sylvester, and B$\acute{e}$zout. In this paper we discuss the historical reflection about the development of solving system of polynomials. We add a special emphasis on E. B$\acute{e}$zout who gave the first account on the resultant which is a generalization of discriminant and Gauss elimination method.

• Ocean Systems Engineering
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• v.11 no.1
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• pp.59-81
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• 2021

The nonlinear formulation using the principle of virtual work-energy for free vibration of a large-sag extensible catenary riser in two dimensions is presented in this paper. A support at one end is hinged and the other is a free-sliding roller in the horizontal direction. The catenary riser has a large-sag configuration in the static equilibrium state and is assumed to displace with large amplitude to the motion state. The total virtual work of the catenary riser system involves the virtual strain energy due to bending, the virtual strain energy due to axial deformation, the virtual work done by the effective weight, and the inertia forces. The nonlinear equations of motion for two-dimensional free vibration in the Cartesian coordinate system is developed based on the difference between the Euler's equations in the static state and the displaced state. The linear and nonlinear stiffness matrices of the catenary riser are obtained and the eigenvalue problem is solved using the Galerkin finite element procedure. The natural frequencies and mode shapes are obtained. The results are validated with regard to the reference research addressing the accuracy and efficiency of the proposed nonlinear formulation. The numerical results for free vibration and the effect of the nonlinear behavior for catenary riser are presented.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.11
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• pp.165-175
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• 2000

In recent years, it becomes a very important issue to consider the mechanical systems such as high-speed vehicles and railway trains moving on elastic beam structures. In this paper, a general approach, which can predict the dynamic behavior of constrained mechanical system and elastic beam structure, is proposed. Also, various supporting conditions of a foundation support are considered for the elastic beam structures. The elastic structure is assumed to be a nonuniform and linear Bernoulli-Euler beam with proportional damping effect. Combined Differential-Algebraic Equations of motion are derived using multibody dynamics theory and Finite Element Method. The proposed equations of motion can be solved numerically using generalizd coordinate partitioning method and Predictor-Corrector algorithm, which is an implicit multi-step integration method.

• Journal of Korean Society of Environmental Engineers
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• v.28 no.4
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• pp.402-406
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• 2006

N-Nitrosodimethylamine(NDMA) formation was studied as a function of chloramine concentration at a fixed dimethylamine (DMA) concentration of 0.05 mM at pH 7 and 8. Regression equations were developed by molar ratio of chloramine to DMA. The NDMA formation was dependent on molar ratio(chloramine/DMA) and was different when the ratio is less or greater than 1. The formation of NDMA increased with increasing chloramine concentration and a linear correlation was examined between NDMA concentration and the ratio on a log scale. The developed regression was applied to previously reported data and relative errors ranged from -79 to 163%. Regression equations could provide a potential tool to predict NDMA formation for a simple and quick estimation in water supply systems.