• Steel and Composite Structures
• /
• v.26 no.5
• /
• pp.649-662
• /
• 2018

In this study, based on the three-dimensional theory of elasticity, free vibration characteristics of sandwich sectorial plates with multiwalled carbon nanotube-(MWCNT)-reinforced composite core are considered. Modified Halpin-Tsai equation is used to evaluate the Young's modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. In this paper, free vibration of thick functionally graded sandwich annular sectorial plates with simply supported radial edges and different circular edge conditions including simply supported-clamped, clamped-clamped, and free-clamped is investigated. A semi-analytical approach composed of two-dimensional differential quadrature method and series solution are adopted to solve the equations of motion. The material properties change continuously through the core thickness of the plate, which can vary according to a power-law, exponentially, or any other formulations in this direction. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated sectorial plates.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
• /
• 1999.11a
• /
• pp.146-153
• /
• 1999

A numerical dynamic simulation is necessary to investigate the capacity of the HDD. The slider surface become more and more complicated to make the magnetized area smaller and readback signal stronger. So a numerical dynamic simulation must be preceded to develop a new slider in HDD. The dynamic simulations of air-lubricated slider bearing have been peformed using FIFD(Factored Implicit Finite Difference) method. The governing equation, Reynolds equation Is modified with Fukui and Kaneko model(FK model) which includes the first and the second-order slip. The equations of motion for the slider bearing are solved simultaneously with the modified Reynolds equation for the case of three degrees of freedom. The slider transient response for disk step bump and slider impulse force is given for various case and for iteration algorithm and new algorithm.

• Journal of applied mathematics & informatics
• /
• v.8 no.2
• /
• pp.581-590
• /
• 2001

In this paper we prove a local stability of Gavruta’s theorem for the generalized Hyers-Ulam-Rassias Stability of Cauchy functional equation.

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.437-446
• /
• 1997

In this paper, the Hyers-Ulam stability and the general Hyers-Ulam stability (more precisely, modified Hyers-Ulam-Rassias stability) of the gamma functional equation (3) in the following setings $$ \left$\mid$ f(x + 1) - xf(x) \right$\mid$ \leq \delta and \left$\mid$ \frac{xf(x)}{f(x + 1)} - 1 \right$\mid$ \leq \frac{x^{1+\varepsilon}{\delta} $$ shall be proved.

• Journal of the Korean Statistical Society
• /
• v.26 no.1
• /
• pp.23-30
• /
• 1997

We show that the Maximum Penalized Likelihood Estimate uniquely exits in a Sobolve spece which consists of bivariate density functions. The Maximum Penalized Likehood Estimate is represented as the square of the sum of the solutions of the Modified Helmholtz's equation on the compact subset of R$^{2}$.

• Communications of the Korean Mathematical Society
• /
• v.15 no.1
• /
• pp.173-181
• /
• 2000

The objective of this paper is to study two dimensional steady gravitational waves on the interface between two immiscible, inviscid and incompressible fluids bounded above by a horizontal rigid boundary and below by a rigid step. A KdV equation for the first order perturbation in an asymptotic expansion can appear. However the coefficient of the KdV theory fails in that case. By a unified asymptotic method, we overcome this difficulty and derive a modified KdV equation with forcing. We find homogeneous steady solutions and present numerical solutions.

• Kyungpook Mathematical Journal
• /
• v.49 no.1
• /
• pp.81-93
• /
• 2009

Bifurcation method of dynamical systems is employed to investigate exact solitary wave solutions and kink wave solutions in the generalized modified Boussinesq equation. Under some parameter conditions, their explicit expressions are obtained. Some previous results are extended.

• The Pure and Applied Mathematics
• /
• v.14 no.4
• /
• pp.279-282
• /
• 2007

Using the center instead of the Lipschitz condition we show how to provide weaker sufficient convergence conditions of the modified Newton Kantorovich method for the solution of nonlinear singular integral equations with Curleman shift (NLSIES). Finer error bounds on the distances involved and a more precise information on the location of the solution are also obtained and under the same computational cost than in [1].

• East Asian mathematical journal
• /
• v.23 no.2
• /
• pp.257-260
• /
• 2007

Using the center instead of the Lipschitz condition we show how to provide weaker sufficient convergence conditions of the modified Newton Kantorovich method for the solution of nonlinear singular integral equations with Curleman shift (NLSIES). Finer error bounds on the distances involved and a more precise information on the location of the solution are also obtained and under the same computational cost than in [1].

• Korean Journal of Agricultural and Forest Meteorology
• /
• v.21 no.4
• /
• pp.238-249
• /
• 2019

The evapotranspiration is estimated based on weather factors such as temperature, wind speed and humidity, and the Hargreaves equation is a simple equation for calculating evapotranspiration using temperature data. However, the Hargreaves equation tends to be underestimated in areas with wind speeds above 3 m s^-1 and overestimated in areas with high relative humidity. The study was conducted to determine Hargreaves equation coefficient in 82 regions in Korea by comparing evapotranspiration determined by modified Hargreaves equation and the Penman-Monteith equation for the time period of 2008~2018. The modified Hargreaves coefficients for 50 inland areas were estimated to be 0.00173~0.00232(average 0.00196), which is similar to or lower than the default value 0.0023. On the other hand, there are 32 coastal areas, and the modified coefficients ranged from 0.00185 to 0.00303(average 0.00234). The east coastal area was estimated to be similar to or higher than the default value, while the west and south coastal areas showed large deviations by area. As results of estimating the evapotranspiration by the modified Hargreaves coefficient, root mean square error(RMSE) is reduced from 0.634~1.394(average 0.857) to 0.466~1.328(average 0.701), and Nash-Sutcliffe Coefficient(NSC) increased from -0.159~0.837(average 0.647) to -0.053~0.910(average 0.755) compared with original Hargreaves equation. Therefore, we confirmed that the Hargreaves equation can be overestimated or underestimated compared to the Penman-Monteith equation, and expected that it will be able to calculate the high accuracy evapotranspiration using the modified Hargreaves equation. This study will contribute to water resources planning, irrigation schedule, and environmental management.