• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.9 no.2
• /
• pp.75-82
• /
• 2005

An inverse problem of transient heat conduction in a thin finite circular plate with the given temperature distribution on the interior surface of a thin circular plate being a function of both time and position has been solved with the help of integral transform technique and also determine the thermal deflection on the outer curved surface of a thin circular plate defined as $0\;{\leq}\;r\;{\leq}\;a,\;0\;{\leq}\;z\;{\leq}\;h$. The results, obtained in the series form in terms of Bessel's functions, are illustrated numerically.

• Proceedings of the KIEE Conference
• /
• 1986.07a
• /
• pp.591-594
• /
• 1986

An asymptotic solution of electro-magnetic waves diffracted by a dielectric wedge of the angle larger than $180^{\circ}$ is obtained in case of the incidence of a E-polarized plane wave. Based on the dual integral equation in the spectral domain, physical optics approximation is supplemented by correction currents distributed along the interfaces. Those currents are expanded in a series of Bessel functions, known as Neumann's expansion of which fractional order is chosen to satisfy the static edge condition as the limiting value of dynamic case. Numerical results of edge diffraction patterns and field patterns are presented for some typical cases.

• Interaction and multiscale mechanics
• /
• v.5 no.1
• /
• pp.13-26
• /
• 2012

In this paper, the wave propagation in a generalized thermo elastic plate embedded in an elastic medium (Winkler model) is studied based on the Lord-Schulman (LS) and Green-Lindsay (GL) generalized two dimensional theory of thermo elasticity. Two displacement potential functions are introduced to uncouple the equations of motion. The frequency equations that include the interaction between the plate and foundation are obtained by the traction free boundary conditions using the Bessel function solutions. The numerical calculations are carried out for the material Zinc and the computed non-dimensional frequency and attenuation coefficient are plotted as the dispersion curves for the plate with thermally insulated and isothermal boundaries. The wave characteristics are found to be more stable and realistic in the presence of thermal relaxation times and the foundation parameter. A comparison of the results for the case with no thermal effects shows well agreement with those by the membrane theory.

• Proceedings of the KSME Conference
• /
• 2004.11a
• /
• pp.649-654
• /
• 2004

A physically simple but mathematically cumbrous problem of rotating heavy chain with one fixed top point is studied. Nonlinear equation of its two-dimensional shapes of relative equilibrium is obtained and solved numerically. A linear case of small displacements is analyzed in terms of Bessel functions. The qualitative and quantitative behavior of the problem is discussed with the help of bifurcation diagram. Dynamics of the two-dimensional model near the equilibrium positions is studied with the help of simulation using the absolute nodal coordinate formulation (ANCF). The equilibriums are found instable, and the reason of instability is explained using a variational principle.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.3
• /
• pp.487-496
• /
• 2002

Hydrodynamic behavior and response of vertical-cylindrical liquid-storage tank is considered. The equation of the liquid motion is shown by Laplace's differential equation with the fluid velocity potential. The solution of the Laplace's differential equation of the liquid motion is expressed with the modified Bessel functions. Only rigid tank is studied. The equivalent masses and heights for the tank contents are presented for engineering design model.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.24 no.4
• /
• pp.317-323
• /
• 2014

This study is concerned with the free vibration analysis of an inextensible uniform rope with a spring-mass system at the tip. The rope is hanged vertically in a gravitational field. This problem is related to the free vibration of an elevator rope connected to an elevator cage. The equation of motion and the corresponding boundary conditions are derived by using the Hamilton's principle. The general solution of the governing equation of motion is expressed in terms of Bessel functions. The characteristic equation was derived by applying the boundary conditions. The characteristic values which are in fact non-dimensionalized natural frequencies were obtained numerically. The effects of mass and spring constant were investigated. The numerical results show how the tip mass and spring affect the natural frequencies of the rope.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
• /
• v.5 no.2
• /
• pp.85-93
• /
• 1993

The rise of a large gas bubble or slug in a Micro Two-Phase Closed Thermosyphon with a thin wire insert has been analiged by the potential flow theory. The effect of the interfacial surface tension is explicitly accounted by application of the Kelvin-Laplace equation and solved for the bubble shape. The solution is expressed in terms of the Stokes stream function which consists of an infinite series of Bessel functions. The conditions of the bubble movement in a Micro Two-Phase Closed Thermosyphon were theoretically ascertained.

• Structural Engineering and Mechanics
• /
• v.46 no.6
• /
• pp.827-842
• /
• 2013

In this paper, the wave propagation in generalized thermo elastic plate immersed in fluid is studied based on the Lord-Shulman (LS) and Green-Lindsay (GL) generalized two dimensional theory of thermo elasticity. Two displacement potential functions are introduced to uncouple the equations of motion. The frequency equations that include the interaction between the plate and fluid are obtained by the perfect-slip boundary conditions using the Bessel function solutions. The numerical calculations are carried out for the material Zinc and the computed non-dimensional frequency, phase velocity and attenuation coefficient are plotted as the dispersion curves for the plate with thermally insulated and isothermal boundaries. The wave characteristics are found to be more stable and realistic in the presence of thermal relaxation times and the fluid interaction.

• Current Optics and Photonics
• /
• v.1 no.6
• /
• pp.649-654
• /
• 2017

In this communication, we present an expression to determine thermal lensing in isotropic materials. The heat equation is analytically solved when a Gaussian spatial laser beam profile is introduced to a cylindrical geometry of optics using a complete set of Bessel functions. This expression permits explicit calculation of variation of focal length induced by thermal lensing and allows thermal effects for various material parameters on the optics. We applied our model to a high absorption material (Ti:sapphire) and also transparent material (thallium garnet or TGG) and found that the thermal lensing can be reduced more than 4 times by adjusting the laser beam waist and optics dimensions. Our analysis is completely general and applicable to any optical system.

• Communications of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1159-1170
• /
• 2018

Recently, Parmar [5] introduced a new extension of the ${\tau}$-Gauss hypergeometric function $_2R^{\tau}_1(z)$. The main object of this paper is to study this extended ${\tau}$-Gauss hypergeometric function and obtain its properties including connection with modified Bessel function of third kind and extended generalized hypergeometric function, several contiguous relations, differential relations, integral transforms and elementary integrals. Various special cases of our results are also discussed.