• 멤브레인
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• 제8권1호
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• pp.1-10
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• 1998

액체 상태에서 물질이 확산되는 현상을 자유 부피의 개념으로 해석하고자 하는 노력은 1959년에 Cohen과 Turnbull에 의해서 시작되었다. 그들은 액체의 부피를 두 부분으로 나누었는데, 하나는 분자가 차지하고 있는 점유 부피(Occupied volume)이고, 다른 하나는 자유 부피(Free-volume)로서 무작정한 열적 유동에 의해서 재분배된다. 온도의 변화에 의해 부피가 변하는 것은 이 자유 부피의 변화때문이며, 점유 부피는 온도에는 무관함 것으로 갖주하였다. 분자가 액체 상태에서 이동하려면 이웃에 충분한 크기의 자유 부피 공간이 존재해야한다. 따라서, 분자의 확산은 분자가 이들 자유 부피 공간들로 도약하는 것이다. Cohen-Turnbull의 이론에서는 순수한 액체의 자기 확산 계수(Self-diffusion conefficient)는 자유 부피의 무작정한 유동에 의하여 임계 크기의 공간이 생성되는 확률과 관련이 있다. Cohen-Turnbull 자유 부피 이론은 그 후 많은 사람들에 의해서 수정되었고, 그중에서 현재 가장 널리 사용되는 것은 Fujita의 이론과 Vrentas-Duda의 이론이다. 두 이론 모두 확산 데이터를 correlation하는데는 문제가 없으나, Vrentas-Duda의 이론만이 확산계수를 예측할 수 있는 능력이 있다. 또한, 고분자와 용매의 도약 단위의 몰 질량이 같을때에 Vrentas-Duda의 이론은 Fujita의 이론과 같아지므로, Fujita의 이론은 Vrentas-Duda의 이론의 특수한 경우라고 할 수 있다. 따라서, 본 논문에서는 Vrentas-Duda 자유 부피 이론만을 다루기로 하겠다.

• Structural Engineering and Mechanics
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• 제70권3호
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• pp.351-365
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• 2019

In this paper, free vibration of Cooper-Naghdi micro sandwich cylindrical shell with saturated porous core and reinforced carbon nanotube (CNT) piezoelectric composite face sheets is investigated by using first order shear deformation theory (FSDT) and modified couple stress theory (MCST). The sandwich shell is subjected to magneto-thermo-mechanical loadings with temperature dependent material properties. Energy method and Hamilton's principle are used for deriving of the motion equations. The equations are solved by Navier's method. The results are compared with the obtained results by the other literatures. The effects of various parameters such as saturated porous distribution, geometry parameters, volume fraction and temperature change on the natural frequency of the micro-sandwich cylindrical shell are addressed. The obtained results reveal that the natural frequency of the micro sandwich cylindrical shell increases with increasing of the radius to thickness ratio, Skempton coefficient, the porosity of the core, and decreasing of the length to radius ratio and temperature change.

• Advances in materials Research
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• 제9권1호
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• pp.63-98
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• 2020

The novelty of this paper is the use of a simple higher order shear and normal deformation theory for bending and free vibration analysis of functionally graded material (FGM) beams on two-parameter elastic foundation. To this aim, a new shear strain shape function is considered. Moreover, the proposed theory considers a novel displacement field which includes undetermined integral terms and contains fewer unknowns with taking into account the effects of both transverse shear and thickness stretching. Different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. In addition, the effect of different micromechanical models on the bending and free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams for which properties vary continuously across the thickness according to a simple power law. Hamilton's principle is used to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio, foundation parameter, the volume fraction of porosity and micromechanical models on the displacements, stresses, and frequencies.

• Bulletin of the Korean Chemical Society
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• 제2권3호
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• pp.90-96
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• 1981

The significant structure theory of liquids has been successfully applied to the sodium ammonia solution. In applying the theory to sodium ammonia solution, we assumed there were four species in solution, i.e., sodium cation, solvated electron, triple ion, and free electron and equilibria existed between them. Based on these assumptions, we set up the model explaining the anomalous properties of sodium ammonia solution. The partition function for sodium ammonia solution is composed of the partition functions for the above four species and also for the Debye-Huckel excess free energy term. Agreements between calculated and experimental values of the thermodynamic quantities, such as molar volume, vapor pressure, partial molar enthalpy and entropy, and chemical potential as well as viscosity are quite satisfactory.

• 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.

• Advances in nano research
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• 제8권4호
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• pp.283-292
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• 2020

In the present research, differential quadrature (DQ) method has been utilized for investigating free vibrations of porous functionally graded (FG) micro/nano beams in thermal environments. The exact location of neutral axis in FG material has been assumed where the material properties are described via porosity-dependent power-law functions. A scale factor related to couple stresses has been employed for describing size effect. The formulation of scale-dependent beam has been presented based upon a refined beam theory needless of shear correction factors. The governing equations and the associated boundary conditions have been established via Hamilton's rule and then they are solved implementing DQ method. Several graphs are provided which emphasis on the role of porosity dispersion type, porosity volume, temperature variation, scale factor and FG material index on free vibrational behavior of small scale beams.

• Steel and Composite Structures
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• 제50권2호
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• pp.135-148
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• 2024

This paper analytically investigates the free vibration analysis of functionally graded-carbon nanotube reinforced composite (FG-CNTRC) plates by dynamic stiffness method (DSM). The properties of CNTRC are determined with the extended rule of mixture. The governing differential equations of motion based on the first-order shear deformation theory of CNTRC plate are derived using Hamilton's principle. The FG-CNTRC plates are studied for a uniform and two different distributions of carbon nanotubes (CNTs). The accuracy and performance of the DSM are compared with the results obtained from closed closed-form and semi-analytical solution methods in previous studies. In this study, the effects of boundary condition, distribution type of CNTs, plate aspect ratio, plate length to thickness ratio, and different values of CNTs volume fraction on the natural frequencies of the FG-CNTRC plates are investigated. Finally, various natural frequencies of the plates in different conditions are provided as a benchmark for comparing the accuracy and precision of the other analytical and numerical methods.

• Structural Engineering and Mechanics
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• 제66권3호
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• pp.353-368
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• 2018

In this work, a high order hyperbolic shear deformation theory with four variables is presented to study the vibratory behavior of functionally graduated plates. The field of displacement of the theory used in this work is introduced indeterminate integral variables. In addition, the effect of porosity is studied. It is assumed that the material characteristics of the porous FGM plate, varies continuously in the direction of thickness as a function of the power law model in terms of volume fractions of constituents taken into account the homogeneous distribution of porosity. The equations of motion are obtained using the principle of virtual work. An analytical solution of the Navier type for free vibration analysis is obtained for a FGM plate for simply supported boundary conditions. A comparison of the results obtained with those of the literature is made to verify the accuracy and efficiency of the present theory. It can be concluded from his results that the current theory is not only accurate but also simple for the presentation of the response of free vibration and the effect of porosity on the latter.

• 대한화학회지
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• 제15권4호
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• pp.171-175
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• 1971

Significant structure theory has been applied to the viscosities of supercooled liquids with success. In the supercooled region, the effect of free volume decrease is so significant that the thermal effects on the solid-like volume must be considered properly. In addition, the two state theories proposed by Jhon and Eyring for water and Litovitz et al. for boron trioxide have been successfully applied to the structure change in the liquid state. Considered liquids are benzene, carbon tetrachloride, p-xylene, water and boron trioxide.

• Coupled systems mechanics
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• 제5권3호
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• pp.269-283
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• 2016

A two new high-order shear deformation theory for bending analysis is presented for a simply supported, functionally graded plate with porosities resting on an elastic foundation. This porosities may possibly occur inside the functionally graded materials (FGMs) during their fabrication, while material properties varying to a simple power-law distribution along the thickness direction. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theories presented are variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. It is established that the volume fraction of porosity significantly affect the mechanical behavior of thick function ally graded plates. The validity of the two new theories is shown by comparing the present results with other higher-order theories. The influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.