• Advances in nano research
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• v.8 no.2
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• pp.135-148
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• 2020

The incorporation of carbon nanotubes in a polymer matrix makes it possible to obtain nanocomposite materials with exceptional properties. It's in this scientific background that this work was based. There are several theories that deal with the behavior of plates, in this research based on the Mindlin-Reissner theory that takes into account the transversal shear effect, for analysis of the critical buckling load of a reinforced polymer plate with parabolic distribution of carbon nanotubes. The equations of the model are derived and the critical loads of linear and parabolic distribution of carbon nanotubes are obtained. With different disposition of nanotubes of carbon in the polymer matrix, the effects of different parameters such as the volume fractions, the plate geometric ratios and the number of modes on the critical load buckling are analysed and discussed. The results show that the critical buckling load of parabolic distribution is larger than the linear distribution. This variation is attributed to the concentration of reinforcement (CNTs) at the top and bottom faces for the X-CNT type which make the plate more rigid against buckling.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.10
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• pp.3371-3380
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• 1996

Low resolution spectral modeling of water vapor is carried out by applying the weighted-sum-of-gray-gases model (WSGGM) to a narrow band. For a given narrow band, focus is placed on proper modeling of gray gas absorption coefficients vs. temeprature relation used for any solution methods for the Radiative Transfer Equation(RTE). Comparison between the modeled emissivity and the "true" emissivity obtained from a high temperatue statistical narrow band parameters is made ofr the total spectrum as well as for a few typical narrow bands. Application of the model to nonuniform gas layers is also made. Low resolution spectral intensities at the boundary are obtained for uniform, parabolic and boundary layer type temeprature profiles using the obtained for uniform, parabolic and boundary layer type temperature profiles using the obtained WSGGM's with 9 gray gases. The results are compared with the narrow band spectral intensities as obtained by a narrow band model-based code with the Curtis-Godson approximation. Good agreement is found between them. Local heat source strength and total wall heat flux are also compared for the cases of Kim et al, which again gives promising agreement.

• Journal of electromagnetic engineering and science
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• v.12 no.1
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• pp.45-54
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• 2012

When the cylindrical wave is incident on a plane dielectric interface from a denser medium to a rarer one, the asymptotic solution for the transmitted wave in the near region is different from the one in the far region. In this paper, we have derived a novel uniform asymptotic solution represented by using the parabolic cylinder function for the transmitted and scattered waves observed in the rarer medium when the cylindrical wave is incident on the plane dielectric interface from the denser medium. The validity of the uniform asymptotic solution has been confirmed by comparing with the reference solution calculated numerically. It has been clarified that the transition wave plays an important role to connect smoothly the asymptotic solution in the near region to the one in the far region through the transition region. We have shown the very interesting phenomenon that the lateral wave type transmitted wave is observed in the far and shallow region.

• Steel and Composite Structures
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• v.50 no.1
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• pp.25-43
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• 2024

In this article, a mathematical model is developed to predict the dynamic behavior of bio-inspired composite beam with helicoidal orientation scheme under variable axial load using a unified higher order shear deformation beam theory. The geometrical kinematic relations of displacements are portrayed with higher parabolic shear deformation beam theory. Constitutive equation of composite beam is proposed based on plane stress problem. The variable axial load is distributed through the axial direction by constant, linear, and parabolic functions. The equations of motion and associated boundary conditions are derived in detail by Hamilton's principle. Using the differential quadrature method (DQM), the governing equations, which are integro-differential equations are discretized in spatial direction, then they are transformed into linear eigenvalue problems. The proposed model is verified with previous works available in literatures. Parametric analyses are developed to present the influence of axial load type, orthotropic ratio, slenderness ratio, lamination scheme, and boundary conditions on the natural frequencies of composite beam structures. The present enhanced model can be used especially in designing spacecrafts, naval, automotive, helicopter, the wind turbine, musical instruments, and civil structures subjected to the variable axial loads.

• The Journal of the Korea institute of electronic communication sciences
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• v.11 no.4
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• pp.411-420
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• 2016

Efforts have continued in recent years to research and develop new alternative energy sources to replace coal and oil. These days interest is exploding in new pollution-free renewable energy due to the rising prices of finite energy sources. In the field of solar energy, one of new renewable energy that has been actively researched and commercialized, research efforts have been focused on solar light energy, whose efficiency has, however, reached a saturation point already. Thus, this paper proposed a solar tracking-type parabolic heat collection device to utilize solar thermal energy rather than solar light energy. The proposed device was designed in a parabolic form to collect solar heat effectively. The investigator made its prototype by incorporating a five-axis censor-based solar tracking technology in it to sense changes to the location of the sun according to the seasons and periods. In addition, an administrator interface was designed and implemented for the efficient management of heat collection device.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.8 no.3
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• pp.246-255
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• 1996

A mild slope equation of parabolic type is derived with the revision of the 2nd order differential term and a new approach for the application to large area is presented. The replacement with long waves can overcome the numerical difficulty due to small waves over the system of large grid sizes. No matter how long the replaced wave length is, the refraction and shoaling are maintained by toeing its own wave speed and group velocity, respectively. However, the diffraction effect is modified by means of Eikonal equation. The developed numerical model was applied to the shoal of Ito and Tanimoto (1972) to yield the satisfactory results.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1061-1067
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• 2013

In this paper, we study surfaces of revolution without parabolic points in 3-Euclidean space $\mathbb{R}^3$, satisfying the condition ${\Delta}^{II}G=f(G+C)$, where ${\Delta}^{II}$ is the Laplace operator with respect to the second fundamental form, $f$ is a smooth function on the surface and C is a constant vector. Our main results state that surfaces of revolution without parabolic points in $\mathbb{R}^3$ which satisfy the condition ${\Delta}^{II}G=fG$, coincide with surfaces of revolution with non-zero constant Gaussian curvature.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.749-761
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• 2018

Here, we calculate the evolution equation of the reduced hh-curvature and the Ricci scalar along the Finslerian Ricci flow. We prove that Finsler Ricci flow preserves positivity of the reduced hh-curvature on finite time. Next, it is shown that evolution of Ricci scalar is a parabolic-type equation and moreover if the initial Finsler metric is of positive flag curvature, then the flag curvature, as well as the Ricci scalar, remain positive as long as the solution exists. Finally, we present a lower bound for Ricci scalar along Ricci flow.

• ETRI Journal
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• v.29 no.6
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• pp.817-819
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• 2007

A low-stress organic polymer membrane is proposed as a deformable mirror that can be incorporated into a cellular phone camera to achieve auto focusing without motor-type moving parts. It is demonstrated that our fabricated device has an optical power of 20 diopters and can switch focus in 14 ms. The surface roughness of the organic membrane is measured around 15 nm, less than ${\lambda}$/20 of the visible light. With curve fitting, we found that the actuated membrane is almost parabolic in shape, which leads to less aberration than spherical surfaces. It is suitable for reflective-optics systems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.41-57
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• 2000

In this paper, we consider first order generalized difference scheme for the two-point boundary value problem and one-dimensional second order parabolic type problem. The optimal error estimates in $L_p$ and $W^{1,p}$ ($2{\leq}p{\leq}{\infty}$) as well as some superconvergence estimates in $W^{1,p}$ ($2{\leq}p{\leq}{\infty}$) are obtained. The main results in this paper perfect the theory of GDM.