• Advances in nano research
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• v.5 no.4
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• pp.281-301
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• 2017

In this disquisition, an exact solution method is developed for analyzing the vibration characteristics of magneto-electro-elastic functionally graded (MEE-FG) beams by considering porosity distribution and various boundary conditions via a four-variable shear deformation refined beam theory for the first time. Magneto-electroelastic properties of porous FG beam are supposed to vary through the thickness direction and are modeled via modified power-law rule which is formulated using the concept of even and uneven porosity distributions. Porosities possibly occurring inside functionally graded materials (FGMs) during fabrication because of technical problem that lead to creation micro-voids in FG materials. So, it is necessary to consider the effect of porosities on the vibration behavior of MEE-FG beam in the present study. The governing differential equations and related boundary conditions of porous MEE-FG beam subjected to physical field are derived by Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factor. An analytical solution procedure is used to achieve the natural frequencies of porous-FG beam supposed to magneto-electrical field which satisfies various boundary conditions. A parametric study is led to carry out the effects of material graduation exponent, porosity parameter, external magnetic potential, external electric voltage, slenderness ratio and various boundary conditions on dimensionless frequencies of porous MEE-FG beam. It is concluded that these parameters play noticeable roles on the vibration behavior of MEE-FG beam with porosities. Presented numerical results can be applied as benchmarks for future design of MEE-FG structures with porosity phases.

• Steel and Composite Structures
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• v.47 no.5
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• pp.633-644
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• 2023

Taking a look at the previously published papers, it is revealed that there is a porosity index limitation (around 0.35) for the mechanical behavior analysis of the functionally graded porous (FGP) structures. Over mentioned magnitude of the porosity index, the elastic modulus falls below zero for some parts of the structure thickness. Therefore, the current paper is presented to analyze the vibrational behavior of the FGP Timoshenko beams (FGPTBs) using a novel refined formulation regardless of the porosity index magnitude. The silica aerogel foundation and various hydrothermal loadings are assumed as the source of external forces. To obtain the FGPTB's properties, the power law is hired, and employing Hamilton's principle in conjunction with Navier's solution method, the governing equations are extracted and solved. In the end, the impact of the various variables as different beam materials, elastic foundation parameters, and porosity index is captured and displayed. It is revealed that changing hygrothermal loading from non-linear toward uniform configuration results in non-dimensional frequency and stiffness pushing up. Also, Al - Al2O3 as the material composition of the beam and the porosity presence with the O pattern, provide more rigidity in comparison with using other materials and other types of porosity dispersion. The presented computational model in this paper hopes to help add more accuracy to the structures' analysis in high-tech industries.

• Journal of Powder Materials
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• v.18 no.2
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• pp.172-175
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• 2011

We developed a 3D simulation model of microstructure evolution of vertically aligned porous structure due to phase separation during film growth. The model proves its validity by reproducing the results of previous researches which are topological features of the microstructures and effects of varied processing parameters. The model will be extended by including bulk diffusion effect and elastic effect.

• Advances in nano research
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• v.7 no.2
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• pp.135-143
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• 2019

The important effect of porosity on the mechanical behaviors of a continua makes it necessary to account for such an effect while analyzing a structure. motivated by this fact, a new two-step porosity dependent homogenization scheme is presented in this article to investigate the wave propagation responses of functionally graded (FG) porous nanobeams. In the introduced homogenization method, which is a modified form of the power-law model, the effects of porosity distributions are considered. Based on Hamilton's principle, the Navier equations are developed using the Euler-Bernoulli beam model. Thereafter, the constitutive equations are obtained employing the nonlocal elasticity theory of Eringen. Next, the governing equations are solved in order to reach the wave frequency. Once the validity of presented methodology is proved, a set of parametric studies are adapted to put emphasis on the role of each variant on the wave dispersion behaviors of porous FG nanobeams.

• Steel and Composite Structures
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• v.41 no.6
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• pp.805-820
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• 2021

In this research, the buckling and free vibration of three-phase carbon nanotubes/ fiber/ polymer piezoelectric nanocomposite face sheet sandwich microbeam with microsensor and micro-actuator surrounded in elastic foundation based on modified couple stress theory (MCST) is investigated. Three types of porous materials are considered for sandwich core. Higher order (Reddy) and sinusoidal shear deformation beam theories are employed for the displacement fields. Sinusoidal surface stress effects are extracted for sinusoidal shear deformation beam theory. The equations of motion are derived by Hamilton's principle and then the natural frequency and critical buckling load are obtained by Navier's type solution. The determined results are in good agreement with other literatures. The detailed numerical investigation for various parameters is performed for this microsensor-microactuator. The results reveal that the microsensor-microactuator enhanced by increasing of Skempton coefficient, carbon nanotubes diameter length to thickness ratio, small scale factor, elastic foundation, surface stress constants and reduction in porous coefficient, micro-actuator voltage and CNT weight fraction. The valuable results can be expedient for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.

• Steel and Composite Structures
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• v.43 no.6
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• pp.821-837
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• 2022

This research is devoted to study the effects of humidity and temperature on the bending behavior of functionally graded (FG) ceramic-metal porous plates resting on Pasternak elastic foundation using a quasi-3D hyperbolic shear deformation theory developed recently. The present plate theory with only four unknowns, takes into account both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the functionally graded plate without using shear correction factors. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. The governing differential equations are obtained using the "principle of virtual work". Analytically, the Navier method is used to solve the equations that govern a simply supported FG porous plate. The obtained results are checked by comparing the results determined for the perfect and imperfect FG plates with those available in the scientific literature. Effects due to material index, porosity factors, moisture and thermal loads, foundation rigidities, geometric ratios on the FG porous plate are all examined. Finally, this research will help us to design advanced functionally graded materials to ensure better durability and efficiency for hygro-thermal environments.

• Korean Journal of Metals and Materials
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• v.49 no.7
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• pp.530-534
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• 2011

To analyze the effect of the pore size of graphite in a pore-forming agent, graphite was added to porous ceramics of $Al_2O_3-SiO_2-ZrO_2$ systems. The graphite had 45~75, 100~125, 150~180, and 75~180${\mu}m$ dimensions. The properties of the ceramics, such as apparent porosity, density, dynamic elastic modulus, mechanical strength, and permeability, were investigated. The average pore size increased from 15.35${\mu}m$ to 22.32${\mu}m$ with the increase of the graphite size. The sample with the largest average pore size showed the highest mechanical strength and gas permeability. This was due to the sample with the largest pore size at the same porosity having fewer pores and larger distance between the pores than the sample with the smallest pore size, making cracks less likely to propagate. In addition, the large pore size reduced the repulsive power originating from the drag force between the gas and internal pore walls.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.634-642
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• 1998

This paper deals with the analytical model of an elastic porous material in sound transmission loss of a double panel with fiber glasses. From the parametric analysis, it is concluded that the boundary condition, which is concerned to the contact between the skin panel and core materials, does not have much influence on sound transmission loss of a double panel with fiber glasses, and material properties of the porous material become, however, important factors to mass-spring-mass resonance. The comparisons of the prediction with the measurement of sound transmission loss of walls show good agreement between the two values.

• Interaction and multiscale mechanics
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• v.4 no.2
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• pp.107-122
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• 2011

Mechanical behavior in nano-sized structures differs from those in macro sized structures due to surface effect. As the ratio of surface to volume increases, surface effect is not negligible and causes size-dependent mechanical behavior. In order to identify this size effect, atomistic simulations are required; however, it has many limitations because too much computational resource and time are needed. To overcome the restrictions of the atomistic simulations and graft the well-established continuum theories, the continuum model considering surface effect, which is based on the bridging technique between atomistic and continuum simulations, is introduced. Because it reflects the size effect, it is possible to carry out a variety of analysis which is intractable in the atomistic simulations. As a part of the application examples, the homogenization method is applied to micro/nano thin films with porosity and the homogenized elastic coefficients of the nano scale thickness porous films are computed in this paper.

• Journal of the Korean Ceramic Society
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• v.48 no.6
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• pp.617-620
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• 2011

Thermal shock behavior of porous ceramic nozzles with various pore sizes for continuous casting process of steel was investigated in terms of physical properties and microstucture. Porous nozzle samples with a composition of $Al_2O_3$-$SiO_2$-$ZrO_2$ were fabricatedby adding various sizes of graphite as the pore forming agent. As the graphite size increased from 45~75 to 150~180 ${\mu}m$, both the resulting pore size and the flexural strength also increased. A thermal shock test was carried out at temperatures (${\Delta}$T) of 600, 700, 800, and 900$^{\circ}C$. Microstructure analysis revealed a small number of cracks on the sample with the largest mean pore size of 22.32 ${\mu}m$. In addition, increasing the pore size led to a smaller decrease in both pressure drop and elastic modulus. In conclusion, controlling the pore size can enhance thermal shock behavior.