• Geomechanics and Engineering
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• v.24 no.3
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• pp.267-280
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• 2021

The research presented in this paper deals with dynamic stability analysis of the graphene nanoplatelets (GPLs) reinforced composite spinning disk. The presented small-scaled structure is simulated as a disk covered by viscoelastic substrate which is two-parametric. The centrifugal and Coriolis impacts due to the spinning are taken into account. The stresses and strains would be obtained using the first-order-shear-deformable-theory (FSDT). For Poisson ratio, as well as various amounts of mass densities, the mixture rule is employed, while a modified Halpin-Tsai model is inserted for achieving the elasticity module. The structure's boundary conditions (BCs) are obtained employing GPLs reinforced composite (GPLRC) spinning disk's governing equations applying principle of Hamilton which is based on minimum energy and ultimately have been solved employing numerical approach called generalized-differential quadrature-method (GDQM). Spinning disk's dynamic properties with different boundary conditions (BCs) are explained due to the curves drawn by Matlab software. Also, the simply-supported boundary conditions is applied to edges 𝜃=𝜋/2, and 𝜃=3𝜋/2, while, cantilever, respectively, is analyzed in R=R_i, and R₀. The final results reveal that the GPLs' weight fraction, viscoelastic substrate, various GPLs' pattern, and rotational velocity have a dramatic influence on the amplitude, and vibration behavior of a GPLRC rotating cantilevered disk. As an applicable result in related industries, the spinning velocity impact on the frequency is more effective in the higher radius ratio's amounts.

• Steel and Composite Structures
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• v.51 no.4
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• pp.377-389
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• 2024

In the present study, thermoelsatoplastic stresses and displacement for rotating hollow disks made of functionally graded materials (FGMs) has been investigated. The linear elastic-fully plastic condition is considered. The material properties except Poisson's ratio are assumed to vary in the radial direction as a power-law function. The heat conduction equation for the one-dimensional problem in cylindrical coordinates is used to obtain temperature distribution in the disk. The plastic model is based on the Tresca yield criterion and its associated flow rules under the assumption of perfectly plastic material behavior. Exact solutions of field equations for elastic and plastic deformations are obtained. It is shown that the elastoplastic response of the functionally graded (FG) disk is affected notably by the radial variation of material properties. It is also shown that, depending on material properties and disk dimensions, different modes of plastic deformation may occur.

• Journal of The Korean Astronomical Society
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• v.37 no.4
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• pp.249-255
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• 2004

Here we present a linear stability analysis and an MHD 2D model for the Parker-Jeans instability in the Galactic gaseous disk. The magnetic field is assumed parallel to a Galactic spiral arm, and the gaseous disk is modelled as a multi-component, magnetized, and isothermal gas layer. The model employs the observed vertical stratifications for the gas density and the gravitational acceleration in the Solar neighborhood, and the self-gravity of the gas is also included. By solving Poisson's equation for the gas density stratification, we determine the vertical acceleration due to self-gravity as a function of z. Subtracting it from the observed gravitational acceleration, we separate the total acceleration into self and external gravities. The linear stability analysis provides the corresponding dispersion relations. The time and length scales of the fastest growing mode of the Parker-Jeans instability are about 40 Myr and 3.3 kpc, respectively. In order to confirm the linear stability analysis, we have performed two-dimensional MHD simulations. These show that the Parker-Jeans instability under the self and external gravities evolves into a quasi-equilibrium state, creating condensations on the northern and southern sides of the plane, in an alternate manner.

• The Journal of the Acoustical Society of Korea
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• v.26 no.2
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• pp.55-60
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• 2007

The shadow, reflection, interference, and diffraction are proper phenomena concerning sound that is a kind of wave. By the late nineteenth century, similar optical phenomena had been detected already but these phenomena concerning sound had not been convincingly detected. It was Rayleigh who succeeded in detecting those phenomena without any reasonable doubt by the virtue of his original instruments and smart experimental settings. Rayleigh could detect the sound shadow by using the corner of a building and erase the shadow by some reflectors. And he constructed some apparatus similar to Young's interference apparatus famous in optics to detect the sonic interference. Furthermore, he first succeeded in illustrating the acoustical effectiveness of Poisson's disk by which optical diffraction had already been well known, and tested the effect of diffraction by spherical obstacles to ascertain that the result coincided with his theory.

• Geophysics and Geophysical Exploration
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• v.25 no.1
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• pp.38-43
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• 2022

In case axial symmetrical bodies with varying cross sections such as volcanic conduits and unexploded ordnance (UXO), it is efficient to approximate them by adding the response of thin disks perpendicular to the axis of symmetry. To compute the vector magnetic and magnetic gradient tensor respones by such bodies, it is necessary to derive an analytical expression of the circular disk. Therefore, in this study, we drive closed-form expressions of the vector magnetic and magnetic gradient tensor due to a circular disk. First, the vector magnetic field is obtained from the existing gravity gradient tensor using Poisson's relation where the gravity gradient tensor due to the same disk with a constant density can be transformed into a magnetic field. Then, the magnetic gradient tensor is derived by differentiating the vector magnetic field with respect to the cylindrical coordinates converted from the Cartesian coordinate system. Finally, both the vector magnetic and magnetic gradient tensors are derived using Lipschitz-Hankel type integrals based on the axial symmetry of the circular disk.

• Journal of The Korean Astronomical Society
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• v.34 no.4
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• pp.285-287
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• 2001

We have studied the nonlinear evolution of a magnetized disk of isothermal gas, which is sustained by its self-gravity. Our objective is to investigate how the Jeans, Parker, and convective instabilities compete with each other in structuring/de-structuring large scale condensations in such disk. The Poisson equation for the self-gravity has been solved with a fourth-order accurate Fourier method along with the Green function, and the MHD part has been handled by an isothermal TVD code. When large wavelength perturbations are applied, the combined action of the Jeans and Parker instabilities suppresses the development of the convection and forms a dense core of prolate shape in the mid-plane. Peripheral structures around it are filamentary. The low density filaments connect the dense core to the diffuse upper region. On the other hand, when small wavelength perturbations are applied, the disk develops into an equilibrium state which is reminiscent of the Mouschovias's 2-D non-linear equilibrium of the classical Parker instability under an externally given gravity.

• Journal of the Korean Vacuum Society
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• v.17 no.6
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• pp.511-517
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• 2008

A quasi two-dimensional model for numerical simulation of gas discharge is presented, based on the finite-element flux-corrected transport method. A one-dimensional continuity convection-diffusion equation coupled Poisson's equation is solved to calculate the charge density variation and the electric field is evaluated by the classical disk method. Results calculated for various benchmark problems verify the accuracy of the proposed model and illustrate its performance. This model has been applied to a streamer simulation, and the results are shown to agree well with previously published results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.1
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• pp.13-23
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• 2015

The paper experimentally deals with the radial in-plane vibration characteristics of disk-shaped piezoelectric transducers. The radial in-plane motion, which is induced due to Poisson's ratio in the piezoelectric disk polarized in the thickness direction, was measured by using an in-plane laser vibrometer, and the natural frequencies were measured by using an impedance analyzer. The experimental results have been compared with theoretical predictions obtained by simplified theoretical and finite-element analyses. It appears that the fundamental mode of a piezoelectric disk transducer is a radial mode and its radial displacement distribution from the center to the perimeter is not monotonic but shows maximum slightly apart from the perimeter. The theoretically-calculated fundamental frequencies agree well with the finite-element results for small thickness-to-diameter ratio, and they are accurate within 7 % error for the ratio up to 0.4.

• Korean Journal of Optics and Photonics
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• v.7 no.4
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• pp.341-347
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• 1996

The photocount distribution from a quasi-thermal light source, a moving ground glass disk (surface roughness; 9 ${\mu}{\textrm}{m}$) illuminated by a well-stabilized He-Ne laser, is measured by a photon counting system, and analyzed with theoretical calculations. The distribution approaches the Poisson distribution for the long coherence time ${\tau}_c$ compared to the measuring time T. The coherence time ${\tau}_c$ of the quasi-thermal source can be changed by controlling the velocity v of the motor driving the glass disk. By the comparison of experimental results and theory for the condition of T/ ${\tau}_c$ >>1, the coherence time ${\tau}_c$ of the quasi-thermal source is turned out to be in the range of 31.43 $mutextrm{s}$~2.48 $mutextrm{s}$ according to the circumferential velocity of the disk, and compared with the simple calculation of $\sigma$/v.

• Steel and Composite Structures
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• v.51 no.2
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• pp.139-151
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• 2024

In this research, a semi-analytical solution is presented for computing mechanical displacements and thermal stresses in rotating thick cylindrical pressure vessels made of functionally graded material (FGM). The modulus of elasticity, linear thermal expansion coefficient, and density of the cylinder are assumed to change along the axial direction as a power-law function. It is also assumed that Poisson's ratio and thermal conductivity are constant. This cylinder was subjected to non-uniform internal pressure and thermal loading. Thermal loading varies in two directions. The governing equations are derived by the first-order shear deformation theory (FSDT). Using the multilayer method, a functionally graded (FG) cylinder with variable thickness is divided into n homogenous disks, and n sets of differential equations are obtained. Applying the boundary conditions and continuity conditions between the layers, the solution of this set of equations is obtained. To the best of the researchers' knowledge, in the literature, there is no study carried out bi-directional thermoelastic analysis of clamped-clamped rotating FGM thick-walled cylindrical pressure vessels under variable pressure in the longitudinal direction.