• Advances in nano research
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• 제10권2호
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• pp.129-138
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• 2021

In present article, utilizing the Love shell theory with volume fraction laws for the cylindrical shells vibrations provides a governing equation for the distribution of material composition of material. Isotopic materials are the constituents of these rings. The position of a ring support has been taken along the radial direction. The Rayleigh-Ritz method with three different fraction laws gives birth to the shell frequency equation. Moreover, the effect of height- and length-to-radius ratio and angular speed is investigated. The results are depicted for circumferential wave number, length- and height-radius ratios with three laws. It is found that the backward and forward frequencies of exponential fraction law are sandwich between polynomial and trigonometric laws. It is examined that the backward and forward frequencies increase and decrease on increasing the ratio of height- and length-to-radius ratio. As the position of ring is enhanced for clamped simply supported and simply supported-simply supported boundary conditions, the frequencies go up. At mid-point, all the frequencies are higher and after that the frequencies decreases. The frequencies are same at initial and final stage and rust itself a bell shape. The shell is stabilized by ring supports to increase the stiffness and strength. Comparison is made for non-rotating and rotating cylindrical shell for the efficiency of the model. The results generated by computer software MATLAB.

• Steel and Composite Structures
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• 제29권1호
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• pp.53-66
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• 2018

A high-order nonlocal strain gradient model is developed for wave propagation analysis of porous FG nanoplates resting on a gradient hybrid foundation in thermal environment, for the first time. Material properties are assumed to be temperature-dependent and graded in the nanoplate thickness direction. To consider the thermal effects, uniform, linear, nonlinear, exponential, and sinusoidal temperature distributions are considered for temperature-dependent FG material properties. On the basis of the refined-higher order shear deformation plate theory (R-HSDT) in conjunction with the bi-Helmholtz nonlocal strain gradient theory (B-H NSGT), Hamilton's principle is used to derive the equations of wave motion. Then the dispersion relation between frequency and wave number is solved analytically. The influences of various parameters (such as temperature rise, volume fraction index, porosity volume fraction, lower and higher order nonlocal parameters, material characteristic parameter, foundations components, and wave number) on the wave propagation behaviors of porous FG nanoplates are investigated in detail.

• Computers and Concrete
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• 제25권5호
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• pp.411-425
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• 2020

In this paper, the shell material has been taken as functionally graded material and their material quantity is located by the exponential volume fraction law. Moreover, the impact of ring supports around the shell circumference has been examined for their various positions along the shell axial length. These rings support restraints the radial displacement in the transverse direction. While the axial modal deformation functions have been estimated by characteristic beam functions and nature of materials used for construction of cylindrical shells. The fundamental natural frequency of cylindrical shell of parameter versus ratios of length- and height-to-radius for a wide range has been reported and investigated through the study. In addition, by increasing height-to-radius ratio resulting frequencies also increase and frequencies decrease on ratio of length-to-radius. Though the trends of frequency values of both ratios are converse to each other with three different boundary conditions. Also it is examined the position of ring supports with length-to radius ratio, height-to-radius ratio and varying the exponent of volume fraction. MATLAB software package has been utilized for extracting shell frequency spectra. The obtained results are confirmed by comparing with available literature.

• Steel and Composite Structures
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• 제42권3호
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• pp.375-388
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• 2022

In this work, limit elastic speed analysis of functionally graded porous rotating disks has been reported. The work proposes an effective approach for modeling the mechanical properties of a porous functionally graded rotating disk. Four different types of porosity models namely: uniform, symmetric, inner maximum, and outer maximum distribution are considered. The approach used is the variational principle, and the solution has been achieved using Galerkin's error minimization theory. The study aims to investigate the effect of grading indices, aspect ratio, porosity volume fraction, and porosity types on limit angular speed for uniform and variable disk geometries of constant mass. To validate the current study, finite element analysis has been used, and there is good agreement between the two methods. The study yielded a decrease in limit speed as grading indices and aspect ratio increase. The porosity volume fraction is found to be more significant than the aspect ratio effect. The research demonstrates a range of operable speeds for porous and non-porous disk profiles that can be used in industries as design data. The results show a significant increase in limit speed for an exponential disk when compared to other disk profiles, and thus, the study demonstrates a range of FG-based structures for applications in industries that will not only save material (lightweight structures) but also improve overall performance.

• 콘크리트학회논문집
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• 제21권1호
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• pp.13-20
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• 2009

본 연구에서는 섬유혼입률이 초고강도 강섬유보강 콘크리트의 인장연화거동 특성에 미치는 영향을 파악하고자 하였다. 노치 낸 보에 대한 3점 재하 휨실험을 통해 초고강도 강섬유보강 콘크리트의 휨인장 거동을 구하고, Uchida 등이 제안한 역해석법을 사용하여 휨 실험 결과로부터 인장연화곡선을 도출하였다. 노치 낸 보의 휨 실험 결과에서 초기강성은 섬유혼입률에 관계없이 일정한 값을 나타내고, 강섬유의 혼입률이 증가할수록 초고강도 강섬유보강 콘크리트의 휨인장강도는 증가하며 연화거동은 일정 균열폭에서 점근적으로 수렴하는 경향을 나타내었다. 역해석을 통해 구한 인장연화곡선으로부터 섬유혼입률과 임계균열폭, $\omega_0$의 함수로 인장연화모델을 제안하였으며, 인장연화모델은 균열이 진행됨에 따라 일정한 인장응력 값을 가지는 소성구간과 지수함수로 주어지는 연화구간으로 나누어 제시하였다. 본 연구에서 제시한 인장연화모델을 적용하여 점성균열모델을 이용한 유한요소해석을 수행한 결과, 해석 결과와 실험 결과와 잘 일치하는 것으로 나타났다.

• Steel and Composite Structures
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• 제25권3호
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• pp.347-360
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• 2017

The goal of this study is to fill this apparent gap in the area about vibration analysis of multiwalled carbon nanotubes (MWCNTs) curved panels by providing 3-D vibration analysis results for functionally graded multiwalled carbon nanotubes (FG-MWCNTs) sandwich structure with power-law distribution of nanotube. The effective material properties of the FG-MWCNT structures are estimated using a modified Halpin-Tsai equation. Modified Halpin-Tsai equation was used to evaluate the Young's modulus of MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The exponential shape factor modifies the Halpin-Tsai equation from expressing a straight line to a nonlinear one in the MWCNTs wt% range considered. Also, the mass density and Poisson's ratio of the MWCNT/phenolic composite are considered based on the rule of mixtures. Parametric studies are carried out to highlight the influence of MWCNT volume fraction in the thickness, different types of CNT distribution, boundary conditions and geometrical parameters on vibrational behavior of FG-MWCNT thick curved panels. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including Free, Simply supported and Clamped at the curved edges. For an overall comprehension on 3-D vibration analysis of sandwich panel, some mode shape contour plots are reported in this research work.

• Structural Engineering and Mechanics
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• 제89권2호
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• pp.103-119
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• 2024

The present research investigates the thermodynamically bending behavior of FG sandwich plates, laying on the Winkler/Pasternak/Kerr foundation with various boundary conditions, subjected to harmonic thermal load varying through thickness. The supposed FG sandwich plate has three layers with a ceramic core. The constituents' volume fractions of the lower and upper faces vary gradually in the direction of the FG sandwich plate thickness. This variation is performed according to various models: a Power law, Trigonometric, Viola-Tornabene, and the Exponential model, while the core is constantly homogeneous. The displacement field considered in the current work contains integral terms and fewer unknowns than other theories in the literature. The corresponding equations of motion are derived based on Hamilton's principle. The impact of the distribution model, scheme, aspect ratio, side-to-thickness ratio, boundary conditions, and elastic foundations on thermodynamic bending are examined in this study. The deflections obtained for the sandwich plate without elastic foundations have the lowest values for all boundary conditions. In addition, the minimum deflection values are obtained for the exponential volume fraction law model. The sandwich plate's non-dimensional deflection increases as the aspect ratio increases for all distribution models.

• Structural Engineering and Mechanics
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• 제63권3호
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• pp.401-415
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• 2017

In this article, hygro-thermo-mechanical vibration and buckling of exponentially graded (EG) nanoplates resting on two-parameter Pasternak foundations are studied using the four-unknown shear deformation plate theory. The material properties are presumed to change only in the thickness direction of the EG nanoplate according to two exponential laws distribution. The boundary conditions of the nanoplate may be simply supported, clamped, free or combination of them. To consider the small scale effect on forced frequencies and buckling, Eringen's differential form of nonlocal elasticity theory is employed. The accuracy of the present study is investigated considering the available solutions in literature. A detailed analysis is executed to study the influences of the plate aspect ratio, side-to-thickness ratio, temperature rise, moisture concentration and volume fraction distributions on the vibration and buckling of the nanoplates.

• Steel and Composite Structures
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• 제19권4호
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• pp.829-841
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• 2015

In this paper, a refined exponential shear deformation beam theory is developed for bending analysis of functionally graded beams. The theory account for parabolic variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Contrary to the others refined theories elaborated, where the stretching effect is neglected, in the current investigation this so-called "stretching effect" is taken into consideration. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present shear deformation beam theory, the equilibrium equations are derived from the principle of virtual displacements. Analytical solutions for static are obtained. Numerical examples are presented to verify the accuracy of the present theory.

• Advances in concrete construction
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• 제10권6호
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• pp.499-507
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• 2020

In current study, utilizing the Kelvin's theory with polynomial, exponential and trigonometric volume fraction laws for functionally graded cylindrical shell vibrations. Effects of different parameters for ratios of length- and height-to-radius and angular speed versus fundamental natural frequencies been determined for two categories of cylindrical shells with clamped-free edge condition. By increasing different value of height-to-radius ratio, the resulting backward and forward frequencies increase and frequencies decrease on increasing length-to-radius ratio. Moreover, on increasing the rotating speed, the backward frequencies increases and forward frequencies decreases. The frequencies are same when the cylinder is stationary. The frequencies increases and decreases on changing the constituent materials. The frequency results are verified with the earlier literature for the applicability of present model.