• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 1996년도 The Korean Institute of Navigation 1996년도 춘계학술발표회 논문집
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• pp.77-92
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• 1996

When an automatic course-keeping is concerned as is quite popular in modern navigation the closed-loop steering system consists of autopilot device power unit (or telemotor unit) steering gear magnetic or gyro compass and ship dynamics. The consideration of irregular disturbances to ship dyanmics and a few non-linear mechanisms involved in the system inevitably or artificially are known to be very important in properly evaluating or analyzing the automatic steering system. In the present study the mathematical model of each element of an automatic steering system is derived which takes account of a fex non-linear mechanisms. PD(Proportional-Derivative) controller and low-pass filter with a weather adjustment are adopted to modelling the characteristics of an autopilot. The calculation method of imposing irregular disturbances to ship dynamics is proposed where irregular disturbances implying irregular wave and the fluctuating component of wind. For he evaluation of automatic steering system of ships in the open seas an important term "performance index" is introduced from the viewpoint of energy saving which derived from the concept of energy loss on ship propulsion. Finally the present methods are applied to two typical types of ship ; an ore carrier and a fishing boat. The various effects of linear and/or non-linear control constants of autopilot on propulsive energy loss are investigated to validate and clarify the present smulation technique.

• Structural Engineering and Mechanics
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• 제16권2호
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• pp.153-176
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• 2003

From the equation of motion of a "bare" non-uniform beam (without any concentrated elements), an eigenfunction in term of four unknown integration constants can be obtained. When the last eigenfunction is substituted into the three compatible equations, one force-equilibrium equation, one governing equation for each attaching point of the concentrated element, and the boundary equations for the two ends of the beam, a matrix equation of the form [B]{C} = {0} is obtained. The solution of |B| = 0 (where ${\mid}{\cdot}{\mid}$ denotes a determinant) will give the "exact" natural frequencies of the "constrained" beam (carrying any number of point masses or/and concentrated springs) and the substitution of each corresponding values of {C} into the associated eigenfunction for each attaching point will determine the corresponding mode shapes. Since the order of [B] is 4n + 4, where n is the total number of point masses and concentrated springs, the "explicit" mathematical expression for the existing approach becomes lengthily intractable if n > 2. The "numerical assembly method"(NAM) introduced in this paper aims at improving the last drawback of the existing approach. The "exact"solutions in this paper refer to the numerical results obtained from the "continuum" models for the classical analytical approaches rather than from the "discretized" ones for the conventional finite element methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권1호
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• pp.27-41
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• 2014

In this paper, we present an efficient numerical method for multiphase image segmentation using a multiphase-field model. The method combines the vector-valued Allen-Cahn phase-field equation with initial data fitting terms containing prescribed interface width and fidelity constants. An efficient numerical solution is achieved using the recently developed hybrid operator splitting method for the vector-valued Allen-Cahn phase-field equation. We split the modified vector-valued Allen-Cahn equation into a nonlinear equation and a linear diffusion equation with a source term. The linear diffusion equation is discretized using an implicit scheme and the resulting implicit discrete system of equations is solved by a multigrid method. The nonlinear equation is solved semi-analytically using a closed-form solution. And by treating the source term of the linear diffusion equation explicitly, we solve the modified vector-valued Allen-Cahn equation in a decoupled way. By decoupling the governing equation, we can speed up the segmentation process with multiple phases. We perform some characteristic numerical experiments for multiphase image segmentation.

• Membrane and Water Treatment
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• 제9권3호
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• pp.173-179
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• 2018

Microcystin-LR, one of algal toxins induced by the eutrophication of a reservoir, is known to be harmful to human by adversely affecting our liver and brain. Hypochlorous acid is very efficient to remove Microcystin-LR in a clear well. The previous researches showed that CT, pH and temperature affected removal rate in batch tests. It was noted that hydrodynamic properties of clear well could also influence its removal rate. A mathematical model was built using an axial dispersion reactor model and software was used to simulate the removal rate. The model consisted of the second order differential equations including dispersion, convection, Microcystin-LR reaction with chlorine. Kinetic constants were obtained through batch tests with chlorine. They were $0.430{\times}10^{-3}L/mg/sec$ and $0.143{\times}10^{-3}L/mg/sec$ for pH 7.0 and 8.1, respectively. The axial dispersion reactor model was shown to be useful for the numerical model through conservative tracer tests. The numerical model successfully estimated the removal rate of Microcyctin-LR in a clear well. Numerical simulations showed that a small dispersion number, low pH and long hydraulic retention time were critical for higher removal rate with same chlorine dosage. This model could be used to optimize the operation of a clear well during an eutrophication season.

• 상하수도학회지
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• 제10권4호
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• pp.103-110
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• 1996

Excessive phosphorus (P as orthophosphate) is one of the major pollutants in natural water that are responsible for algal blooms and eutrophication. P removal by slag is an attractive solution if the P sorption capacity of the slag is significant. To design an efficient land treatment facility, basic information on the behaviour of P in the media-water environment is required. In this study, detailed column experiments were conducted to study the P transport under dynamic condition, and mathematical models were developed to describe this process. The column experiments conducted with dust and cake waste products (slag) from BHP steel industry in Australia as adsorbing media indicated that they had higher sorption capacity of P than that of a sandy loam soil from North Sydney, Australia. P transport in the dust and cake columns exhibited characteristics S-shaped or curvilinear breakthrough curves. The simulated results from a dynamic physical non-equilibrium sorption model (DPNSM) and Freundlich isotherm constants satisfactorily matched the corresponding experimental breakthrough data. The mobility of P is restricted proportionally to the adsorbent's sorption capacity.

• 상하수도학회지
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• 제27권6호
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• pp.815-826
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• 2013

Using a developed mathematical model and calibrated kinetic constants, numerical experiments for a aerobic digestion of wastewater sludge by SBR aerobic digestion process combined with ultrasonication (USSBR) were performed in this study. It simulated well the phenomena of the decomposition of particulate organics and the release of organic nitrogen and transformation. To achieve 40 % of particulate organics removal, USSBR process requires only 6 days of SRT and 14 W/L of ultrasonic power whereas SBR aerobic digestion process requires 12 days of SRT. Based on the model simulation results, an empirical equation was presented here. This equation will be used to predict digestion efficiency for the given variables of SRT and ultrasonic power dose. USSBR aerobic digestion process can reduce the nitrogen concentration. The optimal operation strategy for the simultaneous removal of solids and soluble nitrogen in this process is estimated to 7 days of SRT with 14 W/L of ultrasonic power dose while anoxic period was 6 hours out of 24 hours of cycle time. In this condition, 40 % of particulate organics as well as 36 % of total nitrogen will be removed and the soluble nitrogen concentration of the centrate will be lower less then 40 mg/L.

• Smart Structures and Systems
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• 제2권3호
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• pp.209-224
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• 2006

The use of smart dampers to optimally control the response of structures is on the increase. To maximize the potential use of such damper systems, their accurate modeling and assessment of their performance is of vital interest. In this study, the performance of a controllable fluid dashpot damper, in terms of damper forces, damper dynamic range and damping force hysteretic loops, respectively, is studied mathematically. The study employs a damper Bingham-Maxwell (BingMax) model whose mathematical formulation is developed using a Fourier series technique. The technique treats this one-dimensional Navier-Stokes's momentum equation as a linear superposition of initial-boundary value problems (IBVPs): boundary conditions, viscous term, constant Direct Current (DC) induced fluid plug and fluid inertial term. To hold the formulation applicable, the DC current level to the damper is supplied as discrete constants. The formulation and subsequent simulation are validated with experimental results of a commercially available magneto rheological (MR) dashpot damper (Lord model No's RD-1005-3) subjected to a sinusoidal stroke motion using a 'SCHENK' material testing machine in the Materials Laboratory at the University of Technology, Sydney.

• Structural Engineering and Mechanics
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• 제43권5호
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• pp.561-582
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• 2012

Despite popularity of FEM in analysis of static and dynamic structural problems and the routine applicability of FE softwares, analytical methods based on simple mathematical relations is still largely sought by many researchers and practicing engineers around the world. Development of such analytical methods for analysis of free vibration of non-prismatic beams is also of primary concern. In this paper a new and simple method is proposed for determination of vibration frequencies of non-prismatic beams under variable axial forces. The governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single variable equation in terms of location. Through repetitive integrations, integral equation for the weak form of governing equation is derived. The integration constants are determined using the boundary conditions applied to the problem. The mode shape functions are approximated by a power series. Substitution of the power series into the integral equation transforms it into a system of linear algebraic equations. Natural frequencies are determined using a non-trivial solution for system of equations. Presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic beams. The efficiency and convergence rate of the current approach are investigated through comparison of the numerical results obtained to those obtained using available finite element software.

• Steel and Composite Structures
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• 제50권4호
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• pp.403-418
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• 2024

In this paper, vibration and energy absorption characteristics of a nanostructure which is composed of two embedded porous annular/circular nanoplates coupled by a viscoelastic substrate are investigated. The modified couple stress theory (MCST) and the Gurtin-Murdoch theory are applied to take into account the size and the surface effects, respectively. Furthermore, the structural damping effect is probed by the Kelvin-Voigt model and the mathematical model of the problem is developed by a new hyperbolic higher order shear deformation theory. The differential quadrature method (DQM) is employed to obtain the out-of-phase and in-phase frequencies of the structure in order to predict the dynamic response of it. The acquired results reveal that the vibration and energy absorption of the system depends on some factors such as porosity, surface stress effects, material length scale parameter, damping and spring constants of the viscoelastic foundation as well as geometrical parameters of annular/circular nanoplates. A bird's-eye view of the findings in the research paper offers a comprehensive understanding of the vibrational behavior and energy absorption capabilities of annular/circular porous nanoplates. The multidisciplinary approach and the inclusion of porosity make this study valuable for the development of innovative materials and applications in the field of nanoscience and engineering.

• Structural Engineering and Mechanics
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• 제91권4호
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• pp.417-426
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• 2024

Nanotechnology has emerged as a promising avenue for enhancing musical structures. In this study, we analyze the static behavior of laser harp (i.e., electronic musical instrument) reinforced with Zinc Oxide (ZnO) nanoparticles. Leveraging the piezoelectric properties of ZnO nanoparticles, the structure is subjected to an electric field for intelligent control. The electronic musical structure is situated in a foundation with vertical springs and shear modulus constants. We employ the exponential Shear Deformation Beam Theory (ESDBT) to mathematically model the structure. A micro-electro-mechanical model is employed to determine the equivalent properties of the system. By utilizing nonlinear stress-strain relations, energy methods, and Hamilton's principle, we derive the motion equations. The buckling load of the electronic musical beam is calculated using the Difference Quadrature Method (DQM). The primary objective of this study is to present a mathematical model for electronic musical beams and determining the buckling load of the structure and to investigate the influence of nanotechnology and electric fields on its buckling behavior. The buckling is the case when the structure becomes deforms and unstable. Our findings reveal that the application of negative external voltage to the electronic musical structure increases both the stiffness and the buckling load of the musical system. Furthermore, reinforcing the electronic musical structure with ZnO nanoparticles results in an increased buckling load. Notably, the maximum enhancement in the 28-day compressive and tensile strengths of samples containing zinc oxide nanoparticles compared to the control sample resulting in increases of 18.70% and 3.77%, respectively.