• Earthquakes and Structures
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• v.13 no.5
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• pp.465-471
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• 2017

This work derives a generalized time fractional differential equation governing wave propagation in a radially vibrating non-classical cylindrical medium. The cylinder is made of a transversely isotropic hyperelastic John's material which obeys frequency-dependent power law attenuation. Employing the definition of the conformable fractional derivative, the solution of the obtained generalized time fractional wave equation is expressed in terms of product of Bessel functions in spatial and temporal variables; and the resulting wave is characterized by the presence of peakons, the appearance of which fade in density as the order of fractional derivative approaches 2. It is obtained that the transversely isotropic structure of the material of the cylinder increases the wave speed and introduces an additional term in the wave equation. Further, it is observed that the law relating the non-zero components of the Cauchy stress tensor in the cylinder under consideration generalizes the hypothesis of plane strain in classical elasticity theory. This study reinforces the view that fractional derivative is suitable for modeling anomalous wave propagation in media.

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

• Structural Engineering and Mechanics
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• v.74 no.2
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• pp.215-225
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• 2020

Thin films easily wrinkle under compressive loading due to their small bending stiffness resulting from their tiny thickness. For a thin film deposited on a functionally graded substrate with non-uniform stiffness exponentially changes along the length span in this paper, the uniaxial wrinkling problem is solved analytically in terms of hyper-Bessel functions. For infinite, semi-infinite and finite length systems the wrinkling load and wrinkling wavenumber are determined and compared with those in literature. In comparison with a homogeneous substrate-bounded film in which the wrinkling pattern is uniform along the length span, for a functionally graded substrate-film system the wrinkles accumulate around the softer location of the functionally graded substrate. Therefore, the effective length of the film influenced by the wrinkles decreases, the amplitude of the wrinkles on softer regions of the functionally graded substrate grows and the wrinkling load of the functionally graded substrates with higher softening rate decreases more. The results of the current research are expected to be useful in science and technology of thin films and wrinkling of the structures especially living tissues.

• Bulletin of the Korean Chemical Society
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• v.18 no.4
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• pp.424-427
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• 1997

To study the NMR chemical shift arising from the 5f-electron orbital angular momentum and the 5f-electron spin dipolar-nuclear spin angular momentum interactions, the evaluation of the hyperfine integrals has been extended to any pairs of SCF type 5f orbitals adopting a general method which is applicable to a general vector R, pointing in any direction in space. From the electronic wavefunctions for 5f orbitals expressed in common coordinate system, the radial part of the hyperfine interaction integrals are derived by translating the exponential part, r2 exp(-2βr), in terms of R, rN and the modified Bessel functions. The radial integals for 5f orbitals are tabulated in analytical forms. When two of the hyperfine integrals along the (100), (010), (001), (110), and (111) axes are calculated using the derived radial integrals, the calculated values for the 5f system change sign for R-values larger than R　0.35 nm. But the calculated values for the 4f systems change sign for R-values larger than R　0.20 nm.

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

• Computers and Concrete
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• v.23 no.5
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• pp.303-309
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• 2019

This study investigates axisymmetric fractional vibration of an isotropic hyperelastic semi-linear thin disc with a view to examine effects of finite deformation associated with the material of the disc and effects of fractional vibration associated with the motion of the disc. The generalized three-dimensional equation of motion is reduced to an equivalent time fraction one-dimensional vibration equation. Using the method of variable separable, the resulting equation is further decomposed into second-order ordinary differential equation in spatial variable and fractional differential equation in temporal variable. The obtained solution of the fractional vibration problem under consideration is described by product of one-parameter Mittag-Leffler and Bessel functions in temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem in literature. Finally, and amongst other things, the Cauchy's stress distribution in thin disc under finite deformation exhibits nonlinearity with respect to the displacement fields whereas in infinitesimal deformation hypothesis, these stresses exhibit linear relation with the displacement field.

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

• JSTS:Journal of Semiconductor Technology and Science
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• v.11 no.2
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• pp.111-120
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• 2011

A two-dimensional analytical model for deriving the threshold voltage of a short channel fully depleted (FD) cylindrical/surrounding gate MOSFET (CGT/SGT) is suggested. By taking into account the lateral variation of the surface potential, introducing the natural length expression, and using the Bessel functions of the first and the second kinds of order zero, we can derive potentials in the gate oxide layer and the silicon core fully two-dimensionally. Making use of these potentials, the minimum surface potential can be obtained to derive the threshold voltage as a closed-form expression in terms of various device parameters and applied voltages. Obtained results can be used to explain the drain-induced threshold voltage roll-off of a CGT/SGT in a unified manner.

• Wind and Structures
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• v.28 no.6
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• pp.347-354
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• 2019

This study provides an approximate analytical solution to the fractional vibration problem of thin plate governing anomalous motion of plate subjected to in-plane loads. The method of variable separable is employed to transform the fractional partial differential equations under consideration into a fractional ordinary differential equation in temporal variable and a bi-harmonic plate equation in spatial variable. The technique of conformable fractional derivative is utilized to solve the resulting fractional differential equation and the approach of finite sine integral transform method is used to solve the accompanying bi-harmonic plate equation. The deflection field which measures the transverse displacement of the plate is expressed in terms of product of Bessel and trigonometric functions via the temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem of thin plate in literature. This work shows that conformable fractional derivative is an efficient mathematical tool for tracking analytical solution of fractional partial differential equation governing anomalous vibration of thin plates.

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