• Steel and Composite Structures
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• v.37 no.5
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• pp.621-632
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• 2020

This research deals with the study of vibrational behavior of armchair and zigzag single-walled carbon nanotubes invoking extended Love shell theory. The effects of different physical and material parameters on the fundamental frequencies are investigated. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of single-walled carbon nanotubes are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. To discretize the governing equation in eigen-value form, wave propagation approach is developed. Complex exponential functions have been used and the axial model depends on boundary condition that has been described at the edges of carbon nanotubes to calculate the axial modal dependence. Computer software MATLAB is utilized for the frequencies of single-walled carbon nanotubes and current results shows a good stability with comparison of other studies.

• Advances in nano research
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• v.9 no.4
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• pp.251-261
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• 2020

In this article, vibration attributes of single walled carbon nanotubes based on Galerkin's method have been investigated. The influence of power law index subjected to different end supports has been overtly examined. Application of the Hamilton's variational principal leads to the formation of partial differential equations. The effects of different physical and material parameters on the fundamental frequencies are investigated for armchair and zigzag carbon nanotubes with clamped-clamped, simply supported and clamped-free boundary conditions. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of Single-Walled Carbon Nanotubes (SWCNTs) are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. MATLAB software package has been utilized for extracting tube frequency spectra. The obtained results are confirmed by comparing with available literature.

• Structural Engineering and Mechanics
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• v.76 no.1
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• pp.129-139
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• 2020

In this piece of work, carbon nanotubes motion equations are framed by Kelvin's method. Employment of the Kelvin's method procedure gives birth to the tube frequency equation. It is also exhibited that the effect of frequencies is investigated by varying the different index of polynomial function. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of single-walled carbon nanotubes are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. Throughout the computation, it is observed that the frequency behavior for the boundary conditions follow as; clamped-clamped, simply supported-simply supported and these frequency curves are higher than that of clamped-free curves. Computer software MATLAB is utilized for the frequencies of single-walled carbon nanotubes.

• Steel and Composite Structures
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• v.50 no.3
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• pp.299-318
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• 2024

The main objective of this paper is to compute the far-field acoustic radiation (sound radiation) of functionally graded plates (FGM) loaded by sinusoidally varying point load subjected to the arbitrary boundary condition is carried out. The governing differential equations for thin functionally graded plates (FGM) are derived using classical plate theory (CPT) and Rayleigh integral using the elemental radiator approach. Four cases, segregated on power-law index k=0,1,5,10, are studied. A novel approach is illustrated to compute sound fields of vibrating FGM plates using the physical neutral surface with an elemental radiator approach. The material properties of the FGM plate for all cases are calculated considering the power law indexes. An in-house MATLAB code is written to compute the natural frequencies, normal surface velocities, and sound radiation fields are analytically calculated using semi-analytical formulation. Ansys is used to validate the computed sound power level. The parametric effects of the power law index, modulus ratios, different constituent of FGM plates, boundary conditions, damping loss factor on the sound power level, and radiation efficiency is illustrated. This work is the benchmark approach that clearly explains how to calculate acoustic fields using a solid layered FGM model in ANSYS ACT. It shows that it is possible to asymptotically stabilize the structure by controlling the intermittent layers' stiffness. It is found that sound fields radiated by the elemental radiators approach in MATLAB, ANSYS and literatures are in good agreement. The main novelty of this research is that the FGM plate is analyzed in the low-frequency range, where the stiffness-controlled region governs the whole analysis. It is concluded that a clamped mono-ceramic FGM plate radiates a lesser sound power level and higher radiation efficiency than a mono-metallic or metal-rich FGM plate due to higher stiffness. It is found that change in damping loss factor does not affect the same constituents of FGM plates but has significant effects on the different constituents of FGM plates.

• Advances in nano research
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• v.13 no.3
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• pp.207-216
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• 2022

In this paper, a novel model is developed for frequency behavior of single walled carbon nanotubes. The governing equation of motion is constructed method based on the Sander theory using Rayleigh-Ritz's method The frequencies enhances on increasing the power law index using simply supported, clamped and clamped free end conditions. The frequency curve for C-F is less than other conditions. It is due to the physical constraints which are applied on the edge of the CNT. It is observed that the C-F boundary condition have less frequencies from the other two conditions. The frequency phenomena for zigzag are insignificant throughout the aspect ratio. Moreover when index of power law is increased then frequencies increases for all boundary conditions. The natural frequency mechanism for the armchair (10, 10) for various values of power law index with different boundary conditions is investigated. Here frequencies decrease on increases the aspect ratio for all boundary conditions. The frequency curves of SS-SS edge condition is composed between the C-C and C-F conditions. The curves of frequency are less significant from small aspect ratio (L/d = 4.86 ~ 8.47) and decreases fast for greater ratios. It is found that the frequencies via aspect ratios, armchair (10, 10) have higher values from zigzag (10, 0). It is due to the material structure which is made by the carbon nanotubes. The power law index have momentous effect on the vibration of single walled carbon nanotubes. The present frequency result is also compared numerically experimentally with Raman Spectroscopy.

• Structural Engineering and Mechanics
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• v.24 no.4
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• pp.447-461
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• 2006

Here, the axisymmetric free flexural vibrations and thermal stability behaviors of functionally graded spherical caps are investigated employing a three-noded axisymmetric curved shell element based on field consistency approach. The formulation is based on first-order shear deformation theory and it includes the in-plane and rotary inertia effects. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. The effective material properties are evaluated using homogenization method. A detailed numerical study is carried out to bring out the effects of shell geometries, power law index of functionally graded material and base radius-to-thickness on the vibrations and buckling characteristics of spherical shells.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.5
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• pp.553-561
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• 2015

The exponential and power law functionally graded material(FGM) theory is reformulated considering the refined shear and normal deformation theory. This theory has ability to capture the both normal deformation effect and exponential and power law function in terms of the volume fraction of the constituents for material properties through the plate thickness. Navier's method has been used to solve the governing equations for all edges simply supported plates on Pasternak elastic foundation. Numerical solutions of vibration analysis of FGM plates are presented using this theory to illustrate the effects of power law index and 3-D theory of exponential and power law function on natural frequency. The relations between 3-D and 2-D higher-order shear deformation theory are discussed by numerical results. Further, effects of (i) power law index, (ii) side-to-thickness ratio, and (iii) elastic foundation parameter on nondimensional natural frequency are studied. To validate the present solutions, the reference solutions are discussed.

• Korean Chemical Engineering Research
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• v.61 no.2
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• pp.312-321
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• 2023

Fluidized beds have been widely used in industrial applications, which in most of them, the operating fluid is non-Newtonian. In this study, the combination of the lattice Boltzmann method (LBM) and the smoothed profile method has been developed for non-Newtonian power-law fluids. The validation of the obtained model were investigated by experimental correlations. This model has been used for numerical studying of changing the operating fluid and geometrical parameters on the expansion behavior in liquid-solid beds with both Newtonian and non-Newtonian fluids. Investigations were performed for seven different geometries, one Newtonian, and two non-Newtonian fluids. The power-law index was in the range of 0.8 to 1, and the results for the Newtonian fluidized beds show more porosity than the non-Newtonian ones. Furthermore, increasing the power-law index resulted in enhancing the bed porosity. On the other hand, bed porosity was decreased by increasing the initial bed height and the density of the solid particles. Finally, the porosity ratio in the bed was decreased by increasing the solid particle diameter.

• Structural Engineering and Mechanics
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• v.77 no.6
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• pp.797-807
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• 2021

A new simple solution for critical buckling of FG sandwich plates under axial and biaxial loads is presented using new modified power-law formulations. Both even and uneven distributions of porosity are taken into account in this study. Material properties of the sandwich plate faces are assumed to be graded in the thickness direction according to a modified power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FG sandwich plate with various boundary conditions are derived using the higher-order shear deformation plate theory. The results reveal that the distribution shape of the porosity, the gradient index, loading type and functionally graded layers thickness have significant influence on the buckling response of functionally graded sandwich plates.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.2
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• pp.42.1-42.1
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• 2015

We model the Spectral Energy Distribution (SED) of Class 0 protostar L1527 IRS using a radiative transfer code RADMC-3D. In addition to the photometry data from literatures, we include the Herschel/PACS data which well covers the far-infrared SED peak of L1527 IRS, providing precise constraints to the density structure and other physical properties of its circumstellar envelope. Previously, Tobin et al. (2013) presented a dust continuum modeling results using a rotating and infalling envelope (Terebey and Shu, & Cassen 1984 ; TSC envelope), which originally describes a power-law density profile (${\rho}{\propto}r-{\alpha}$) with the power-law index (${\alpha}$) of 1.5. However, we find that Herschel/PACS data are better fitted with a shallower power-law density profile. This smaller power-law might be attributed to a inner envelope. Thus, we fit the SED of L1527 IRS with a Bonnor-Ebert sphere, which is a combination of the inner flat-topped and the outer power-law (${\alpha}=2$) density profiles. This Bonnor-Ebert sphere is often used to explain the density profile of prestellar cores, which is considered the earliest stages of star formation. The well-fitted SED with a Bonnor-Ebert sphere suggests that L1527 IRS might have collapsed from a Bonnor-Ebert sphere rather than a singular isothermal sphere.