• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.521-538
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• 2012

In this study, the transverse vibrations of an axially moving flexible beams resting on multiple supports are investigated. The time-dependent velocity is assumed to vary harmonically about a constant mean velocity. Simple-simple, fixed-fixed, simple-simple-simple and fixed-simple-fixed boundary conditions are considered. The equation of motion becomes independent from geometry and material properties and boundary conditions, since equation is expressed in terms of dimensionless quantities. Then the equation is obtained by assuming small flexural rigidity. For this case, the fourth order spatial derivative multiplies a small parameter; the mathematical model converts to a boundary layer type of problem. Perturbation techniques (The Method of Multiple Scales and The Method of Matched Asymptotic Expansions) are applied to the equation of motion to obtain approximate analytical solutions. Outer expansion solution is obtained by using MMS (The Method of Multiple Scales) and it is observed that this solution does not satisfy the boundary conditions for moment and incline. In order to eliminate this problem, inner solutions are obtained by employing a second expansion near the both ends of the flexible beam. Then the outer and the inner expansion solutions are combined to obtain composite solution which approximately satisfying all the boundary conditions. Effects of axial speed and flexural rigidity on first and second natural frequency of system are investigated. And obtained results are compared with older studies.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.11
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• pp.2971-2980
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• 1995

A numerical study of fluid flow in driven cavity was carried out using singular finite element method. The driven cavity problem is known to have infinite velocity gradients as well as dual velocity conditions at the singular points. To overcome such difficulties, a finite element method with singular shape functions was used and a special technique was employed to allow multiple values of velocities at the singular points. Application of singular elements in the driven cavity problem has a significant influence on the stability of solution. It was found the singular elements gave a stable solution, especially, for the pressure distribution of the entire flow field by keeping up a large pressure at the singular points. In the existing solutions of driven cavity problem, most efforts were focused on the study of streamlines and vorticities, and pressure were seldom mentioned. In this study, however, more attention was given to the pressure distribution. Computations showed that pressure decreased very rapidly as the distance from the singular point increased. Also, the pressure distribution along the vertical walls showed a smoother transition with singular elements compared to those of conventional method. At the singular point toward the flow direction showed more pressure increase compared with the other side as Reynolds number increased.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.34 no.2
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• pp.99-103
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• 2010

A new analytic solution was derived for the diffusion into or from an immobile zone of a rectangular 2-D pore. For a long time, the new solution converges to a traditional mobile-immobile zone (MIM) model, but only if the latter is used with an apparent initial concentration that is smaller by almost 20% than the true one. This is the tradeoff for using a simple MIM model instead of an exact model based on the diffusion equation. The mass-transfer coefficient was found to be constant for a sufficiently long time; it was proportional to the molecular diffusion and inversely proportional to the square of the pore depth. The mass-transfer coefficient was time-dependent for a sufficiently short time and may be significantly larger than its asymptotic value.

• Journal of the Korean Geotechnical Society
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• v.31 no.7
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• pp.13-28
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• 2015

This study extended the Lee et al.'s (2015a) solution which improved the existing analytical solution for prediction of the residual pore water pressure into progressive wave and flow coexisting field. At this time, the variation of incident wave period and wave length should be incorporated to Lee et al.'s (2015a) analytical solution, which does not consider flow. For the case of infinite thickness, the new analytical solution using Fourier series was compared to the analytical solution using Laplace transformation proposed by Jeng and Seymour (2007). It was verified that the new solution was identical to the Jeng and Seymour's solution. After verification of the new analytical solution, the residual pore water pressure head was examined closely under various given values of flow velocity's magnitude, direction, incident wave's period and seabed thickness. In each proposed analytical solution, asymptotic approach to shallow depth with the changes in the soil thickness within finite soil thickness was found possible, but not to infinite depth. It is also identified that there exists a discrepancy case between the results obtained from the finite and the infinite seabed thicknesses even on the same soil depth.

• Bulletin of the Society of Naval Architects of Korea
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• v.26 no.4
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• pp.3-13
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• 1989

In recent towing tank experiments, it has been observed that a ship moving near the critical speed $\sqrt{gh}$(g=gravitational acceleration, h=water depth) radiates solitons upstream in an almost periodic manner. As a ,consequence, the ship experiences considerable changes in resistance, trim and sinkage, or better known as squat. Mei and Choi(1987) developed a nonlinear theory for a slender ship by using the method of matched asymptotic expansions. For a certain class of channel width and ship slenderness, they found that the waves generated can be described by an inhomogeneous Korteweg-de Vries(KdV) equation. The leading-order solution properly predicts solitons propagating upstream, but it fails to render three-dimensional waves in the wake. In this paper a new approach has been made by choosing a different class of channel width and ship slenderness. The wave equation in the farfield turns out to be a homogeneous Kadomtsev-Petviashvili(KP) equation, which predicts solitons upstream and three-dimensional waves in the wake. Numerical results for the wave resistance, sinkage and trim reflect the experimentally identified phenomena.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.7
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• pp.767-773
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• 2014

The carrier-to-noise power ratio is a key parameter for determining the reliability of PVT (Position, Velocity, and Time) solutions which are obtained by a GNSS (Global Navigation Satellite System) receiver. It is also used for locking a tracking loop, deciding the re-acquisition process, and processing advanced navigation in the receiver subsystem. The representative carrier-to-noise power ratio estimation schemes are the narrowband-wideband power ratio method (NW), the MM (Moment Method), and Beaulieu's method (BL). The NW scheme is the most classical one for commercial GNSS receivers. It is often used as an authoritative benchmark for assessing carrier-to-noise power estimation schemes. The MM scheme is the least biased solution among them, and the BL scheme is a simpler scheme than the MM scheme. This paper focuses on the less biased estimation with low complexity when the residual phase noise remains, then proposes a novel carrier-to-noise power ratio estimation scheme with low complexity for GNSS receivers. The asymptotic bias of the proposed scheme is derived and compared with others, and the simulation results demonstrate that the complexity of the proposed scheme is lowest among them, while the estimation performance of the proposed scheme is similar to those of the BL and MM schemes in normal and high gained reception environments.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.2
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• pp.89-99
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• 2001

In the present paper, Helmholtz resonator, which is widely used as a sound-amplification device, is applied to the development of seawater-exchanging breakwater. The incident waves can induce a large response in the resonator when incident wave frequency is close to one of natural modes of the resonator. Largely amplified potential energy due to the resonance supplies clean seawater into the harbor side throughout the channel. Flow supplied by the resonator circulates the seawater of harbor and helps to improve water quality. Within the framework of linear potential theory, matched asymptotic expansion method is employed to analyze the wave responses in a resonator. The semi-circular shape of the resonator has been chosen as an analytic model for mathematical simplicity. The wave responses of both single and arrays of Helmholtz resonator are investi¬gated. To validate an analytic solution, model test is conducted at 2-dimensional wave tanle Wave hcights in the resonator and velocity at the channel are measured for the state of valve-on and valve-off.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.181-192
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• 2016

We consider several methods to approximate option prices with correction terms to the Black-Scholes option price. These methods are able to compute option prices from various risk-neutral distributions using relatively small data and simple computation. In this paper, we compare the performance of Edgeworth expansion, A-type and C-type Gram-Charlier expansions, a method of using Normal inverse gaussian distribution, and an asymptotic method of using nonlinear regression through simulation experiments and real KOSPI200 option data. We assume the variance gamma model in the simulation experiment, which has a closed-form solution for the option price among the pure jump $L{\acute{e}}vy$ processes. As a result, we found that methods to approximate an option price directly from the approximate price formula are better than methods to approximate option prices through the approximate risk-neutral density function. The method to approximate option prices by nonlinear regression showed relatively better performance among those compared.

• Smart Structures and Systems
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• v.24 no.1
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• pp.83-94
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• 2019

Passive negative stiffness dampers (NSDs) that possess superior energy dissipation abilities, have been proved to be more efficient than commonly adopted passive viscous dampers in controlling stay cable vibrations. Recently, inertial mass dampers (IMDs) have attracted extensive attentions since their properties are similar to NSDs. It has been theoretically predicted that superior supplemental damping can be generated for a taut cable with an IMD. This paper aims to theoretically investigate the impact of the cable sag on the efficiency of an IMD in controlling stay cable vibrations, and experimentally validate superior vibration mitigation performance of the IMD. Both the numerical and asymptotic solutions were obtained for an inclined sag cable with an IMD installed close to the cable end. Based on the asymptotic solution, the cable attainable maximum modal damping ratio and the corresponding optimal damping coefficient of the IMD were derived for a given inertial mass. An electromagnetic IMD (EIMD) with adjustable inertial mass was developed to investigate the effects of inertial mass and cable sag on the vibration mitigation performance of two model cables with different sags through series of first modal free vibration tests. The results show that the sag generally reduces the attainable first modal damping ratio of the cable with a passive viscous damper, while tends to increase the cable maximum attainable modal damping ratio provided by the IMD. The cable sag also decreases the optimum damping coefficient of the IMD when the inertial mass is less than its optimal value. The theoretically predicted first modal damping ratio of the cable with an IMD, taking into account the sag generally, agrees well with that identified from experimental results, while it will be significantly overestimated with a taut-cable model, especially for the cable with large sag.

• Smart Structures and Systems
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• v.23 no.6
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• pp.537-551
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• 2019

In this paper, a method for analyzing the damping performance of stay cables incorporating magnetorheological (MR) dampers in the passive control mode is developed taking into account the cable sag and inclination, the damper coefficient, stiffness and mass, and the stiffness of damper support. Both numerical and asymptotic solutions are obtained from complex modal analysis. With the asymptotic solution, analytical formulas that evaluate the equivalent damping ratio of the sagged cable-damper system in consideration of all the above parameters are derived. The main thrust of the present study is to develop an general design formula and a universal curve for the optimal design of MR dampers for adjustable passive control of sagged cables. Two sag-affecting coefficients are derived to reflect the effects of cable sag on the maximum attainable damping ratio and the optimal damper coefficient. For the cable configurations commonly used in cable-stayed bridges, the sag-affecting coefficients are directly expressed in terms of the sag-extensibility parameter to facilitate the control design. A case study on adjustable passive vibration control of the longest cable (536 m) on Stonecutters Bridge is carried out to demonstrate the influence of the sag for the damper design, and to figure out the necessity of adjustability of damper coefficients for achieving maximum damping ratio for different vibration modes.