• Steel and Composite Structures
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• v.30 no.6
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• pp.603-615
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• 2019

In the present work, free vibration of beams made of imperfect functionally graded materials (FGMs) including porosities is investigated. Because of faults during process of manufacture, micro voids or porosities may arise in the FGMs, and this situation causes imperfection in the structure. Therefore, material properties of the beams are assumed to vary continuously through the thickness direction according to the volume fraction of constituents described with the modified rule of mixture including porosity volume fraction which covers two types of porosity distribution over the cross section, i.e., even and uneven distributions. The governing equations of power law FGM (P-FGM) and sigmoid law FGM (S-FGM) beams are derived within the frame works of classical beam theory (CBT) and first order shear deformation beam theory (FSDBT). The resulting equations are solved using separation of variables technique and assuming FG beams are simply supported at both ends. To validate the results numerous comparisons are carried out with available results of open literature. The effects of types of volume fraction function, beam theory and porosity volume fraction, as well as the variations of volume fraction index, span to depth ratio and porosity volume fraction, on the first three non-dimensional frequencies are examined in detail.

• Journal of the Korean Ceramic Society
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• v.35 no.9
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• pp.988-994
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• 1998

In the manufacturing of vitreous bonded CBN tool the porosity change associated with various processing conditions, I. e. the sintering temperature and the size and the amount of abrasive grits was observed. In the case of sintering of vitreous bond material only the specimen density reached the maximum at 950$^{\circ}C$ and then the total porosity was increased slightly with the temperature above 950$^{\circ}C$. In the sintering of a-brasive grits and the vitreous bond material together a marked increase in the total porosity was found with the temperature above 950$^{\circ}C$ Reducing the grit size at the constant volume fraction of abrasive grits showed an increase in the total porosity at whole sintering temperature. On the contrary. it was observed that increasing the volume fraction of abrasive grits with a same size showed the increased open porosity simultaneously with decreased closed porosity at whole sintering temperature.

• Journal of Korea Foundry Society
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• v.22 no.4
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• pp.155-159
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• 2002

Magnesium alloys have high strength to weight ratio and are extremely attractive for applications in transport industry. Most of structural magnesium alloys are manufactured by die casting process. The tensile properties of AZ91HP magnesium alloy were investigated after die casting under various die casting conditions. After die casting by using cold chamber machine, the volume porosity of specimens was examined with density method. With the increase of the volume porosity of specimens, both the tensile strength and elongation were significantly decreased, however the 0.2% offset strength was almost independent of the amount of porosity. With the increase of crystal pressure from 500 to 900 bar during die casting, the volume porosity was decreased, which resulted in the increase of the tensile strength. The mould temperature within the range of $150{\sim}250^{\circ}C$ has not influenced the microstructure with the eutectic phase and tensile properties of specimens. The tensile strength was the highest at 90m/sec of gate speed.

• Structural Engineering and Mechanics
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• v.72 no.1
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• pp.61-70
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• 2019

The functionally graded materials (FGM) used in plates contain probably a porosity volume fraction which needs taking into account this aspect of imperfection in the mechanical bahavior of such structures. The present work aims to study the effect of the distribution forms of porosity on the bending of simply supported FG plate reposed on the Winkler-Pasternak foundation. A refined theory of shear deformation is developed to study the effect of the distribution shape of porosity on static behavior of FG plates. It was found that the distribution form of porosity significantly influence the mechanical behavior of FG plates, in terms of deflection, normal and shear stress. It can be concluded that the proposed theory is simple and precise for the resolution of the behavior of flexural FGM plates resting on elastic foundations while taking into account the shape of distribution of the porosity.

• Steel and Composite Structures
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• v.49 no.6
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• pp.713-728
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• 2023

This paper aims to investigate the free vibration analysis of FG plates, taking into account the effects of even and uneven porosity. The study employs the Hellinger-Reisner functional and obtains the element's bending stress and membrane stress fields from the analytical solution of the governing equations of the thick plate and plane problem, respectively. The displacement field serves as the second independent field. While few articles on free vibration analysis of circular plates exist, this paper investigates the free vibration of both rectangular and circular plates. After validating the proposed element, the paper investigates the effects of porosity distributions on the natural frequency of the FG porous plate. The study calculates the natural frequency of thin and thick bending plates with different aspect ratios and support conditions for various porosity and volume fraction index values. The study uses three types of porosity distributions, X, V, and O, for the uneven porosity distribution case. For O and V porosity distribution modes, porosity has a minor effect on the natural frequency for both circular and rectangular plates. However, in the case of even porosity distribution or X porosity distribution, the effect of porosity on the natural frequency of circular and rectangular plates increases with an increase in the volume fraction index.

• Structural Engineering and Mechanics
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• v.82 no.2
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• pp.151-161
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• 2022

In this study, the effect of porosity distribution pattern on the free vibration analysis of porous FG plates with various boundary conditions is studied. The material properties of the plate and the porosities within the plate are considered to vary continuously through the thickness direction according to the volume fraction of constituents defined by the modified rule of the mixture, this includes porosity volume fraction with four different types of porosity distribution over the cross-section. The governing partial differential equation of motion for the free vibration analysis is obtained using hyperbolic shear deformation theory. An analytical solution is presented for the governing PDEs for various boundary conditions. Results of the presented solution are compared and validated by the available results in the literature. Moreover, the effects of material and porosity distribution and geometrical parameters on vibrational properties are investigated.

• Computers and Concrete
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• v.25 no.3
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• pp.215-224
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• 2020

In the present study, according to the important of porosity in low specific weight in comparison of high stiffness of carbon nanotubes reinforced composite, buckling and free vibration analysis of sandwich composite beam in two configurations, of laminates using differential quadrature method (DQM) is studied. Also, the effects of porosity coefficient and three types of porosity distribution on critical buckling load and natural frequency are discussed. It is shown the buckling loads and natural frequencies of laminate 1 are significantly larger than the results of laminate 2. When configuration 2 (the core is made of FRC) and laminate 1 ([0/90/0/45/90]_s) are used, the first natural frequency rises noticeably. It is also demonstrated that the influence of the core height in the case of lower carbon volume fractions is negligible. Even though, when volume fraction of fiber increases, the critical buckling load enhances smoothly. It should be noticed the amount of decline has inverse relationship with the beam aspect ratio. Investigating three porosity patterns, beam with the distribution of porosity Type 2 has the maximum critical buckling load and first natural frequency. Among three elastic foundations (constant, linear and parabolic), buckling load and natural frequency in linear variation has the least amount. For all kind of elastic foundations, when the porosity coefficient increases, critical buckling load and natural frequency decline significantly.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.34 no.5
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• pp.1-17
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• 2002

The immobilization and consolidation of the model coatings based on the plastic pigment and latex binder of known particle sizes were theoretically Studied in terms of the dense random packing of binary spheres and varying extent of latex film shrinkage. The porosity of the model coatings was calculated based on three proposed latex shrinkage models: Maximum, Minimum, and Linearly Decreasing Latex Shrinkage. The increasing extent of latex shrinkage was calculated up to the critical pigment volume concentration(CPVC) as a function of plastic pigment volume fractions, and the maximum latex shrinkage was estimated from the CPVC. Also, the number of pores and the average equivalent spherical pore diameters were calculated based on those proposed models. The opacity and gloss of the model coatings on polyester films were measured and their porosity was also determined by a simple coat weight-thickness method. As expected, various coating structure-property-composition relationships, such as opacity, gloss, porosity, etc., were shown to exhibit sharp transitions near the CPVC. The CPVC values determined by the opacity, gloss, and porosity vs. PVC relationships, respectively, agreed very well with each other. Especially, the CPVC's determined by the opacity and porosity vs. PVC curves were identical. The comparison between the theoretically calculated and experimental porosity values showed that the intermediate value between the maximum and minimum latex shrinkage would best fit the experimental porosity data. The effect of plastic pigment particle size on the optical properties and porosity of model coatings was also studied and it was observed that the coating opacity and porosity increased with increasing plastic pigment particle size, but the gloss decreased. The ink gloss of the uncalendered model coatings applied onto commercial sheet offset coated papers was shown to be affected by both the coating gloss and porosity: the higher the coating gloss, the higher the ink gloss, but the higher the coating porosity, the lower the ink gloss. Their printability was also studied in terms of the number of passes-to-fail and the rate of ink setting as a function of both plastic pigment volume fractions and plastic pigment particle sizes. A minimum crack-free temperature(MCR) of latex-bound coatings was proposed to better predict the behaviors of latexes as coating binders. The wet state of model coating dispersions, the surfaces of consolidated model coatings, and their internal structure were examined by both electron and atomic force microscopy, and their micrographs were found to be consistent with our immobilization and consolidation models.

• Coupled systems mechanics
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• v.9 no.6
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• pp.499-519
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• 2020

The effect of porosity on the thermo-mechanical behavior of simply supported functionally graded plate reposed on the Winkler-Pasternak foundation is investigated analytically in the present paper using new refined hyperbolic shear deformation plate theory. Both even and uneven distribution of porosity are taken into account and the effective properties of FG plates with porosity are defined by theoretical formula with an additional term of porosity. The present formulation is based on a refined higher order shear deformation theory, which is based on four variables and it still accounts for parabolic distribution of the transverse shearing strains and stresses through the thickness of the FG plate and takes into account the various distribution shape of porosity. The elastic foundation is described by the Winkler-Pasternak model. Anew modified power-law formulation is used to describe the material properties of FGM plates in the thickness direction. The closed form solutions are obtained by using Navier technique. The present results are verified in comparison with the published ones in the literature. The results show that the dimensionless and stresses are affected by the porosity volume fraction, constituent volume fraction, and thermal load.

• Earthquakes and Structures
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• v.10 no.6
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• pp.1429-1449
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• 2016

The effect of porosity on bending and free vibration behavior of simply supported functionally graded plate reposed on the Winkler-Pasternak foundation is investigated analytically in the present paper. The modified rule of mixture covering porosity phases is used to describe and approximate material properties of the FGM plates with porosity phases. The effect due to transverse shear is included by using a new refined shear deformation theory. The number of unknown functions involved in the present theory is only four as against five or more in case of other shear deformation theories. The Poisson ratio is held constant. Based on the sinusoidal shear deformation theory, the position of neutral surface is determined and the equation of motion for FG rectangular plates resting on elastic foundation based on neutral surface is obtained through the minimum total potential energy and Hamilton's principle. The convergence of the method is demonstrated and to validate the results, comparisons are made with the available solutions for both isotropic and functionally graded material (FGM). The effect of porosity volume fraction on Al/Al2O3 and Ti-6Al-4V/Aluminum oxide plates are presented in graphical forms. The roles played by the constituent volume fraction index, the foundation stiffness parameters and the geometry of the plate is also studied.