• 제목/요약/키워드: non-linear modulus

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On vibration and flutter of shear and normal deformable functionally graded reinforced composite plates

  • Abdollahi, Mahdieh;Saidi, Ali Reza;Bahaadini, Reza
    • Structural Engineering and Mechanics
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    • v.84 no.4
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    • pp.437-452
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    • 2022
  • For the first time, the higher-order shear and normal deformable plate theory (HOSNDPT) is used for the vibration and flutter analyses of the multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) plates under supersonic airflow. For modeling the supersonic airflow, the linear piston theory is adopted. In HOSNDPT, Legendre polynomials are used to approximate the components of the displacement field in the thickness direction. So, all stress and strain components are encountered. Either uniform or three kinds of non-uniform distribution of graphene platelets (GPLs) into polymer matrix are considered. The Young modulus of the FG-GPLRC plate is estimated by the modified Halpin-Tsai model, while the Poisson ratio and mass density are determined by the rule of mixtures. The Hamilton's principle is used to obtain the governing equations of motion and the associated boundary conditions of the plate. For solving the plate's equations of motion, the Galerkin approach is applied. A comparison for the natural frequencies obtained based on the present investigation and those of three-dimensional elasticity theory shows a very good agreement. The flutter boundaries for FG-GPLRC plates based on HOSNDPT are described and the effects of GPL distribution patterns, the geometrical parameters and the weight fraction of GPLs on the flutter frequencies and flutter aerodynamic pressure of the plate are studied in detail. The obtained results show that by increasing 0.5% of GPLs into polymer matrix, the flutter aerodynamic pressure increases approximately 117%, 145%, 166% and 196% for FG-O, FG-A, UD and FG-X distribution patterns, respectively.

Comparative Compressional Behavior of Zeolite-W in Different Pressure-transmitting Media (제올라이트-W의 압력전달매개체에 따른 체적탄성률 비교 연구)

  • Seoung, Donghoon;Kim, Hyeonsu;Kim, Pyosang;Lee, Yongmoon
    • Korean Journal of Mineralogy and Petrology
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    • v.34 no.3
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    • pp.169-176
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    • 2021
  • This study aimed to fundamentally understand structural changes of zeolite under pressure and in the presence of different pressure-transmitting media (PTM) for application studies such as immobilization of heavy metal cation or CO2 storage using pressure. High-pressure X-ray powder diffraction study was conducted on the zeolite-W (K6.4Al6.5Si25.8O64× 15.3H2O, K-MER) to understand linear compressibility and the bulk moduli in different PTM conditions. Zeolite-w is a synthetic material having the same framework as natural zeolite merlinoite ((K, Ca0.5, Ba0.5, Na)10 Al10Si22O64× 22H2O). The space group of the sample was identified as I4/mmm belonging to the tetragonal crystal system. Water, carbon dioxide, and silicone-oil were used as pressure-transmitting media. The mixture of sample and each PTM was mounted in a diamond anvil cell (DAC) and then pressurized up to 3 GPa with an increment of ca. 0.5 GPa. Pressure-induced changes of powder diffraction patterns were measured using a synchrotron X-ray light source. Lattice constants, and bulk moduli were calculated using the Le-Bail method and the Birch-Murnaghan equation. In all PTM conditions, linear compressibility of c-axis (𝛽c) was 0.006(1) GPa-1 or 0.007(1) GPa-1. On the other hand, the linear compressibility of a(b)-axis (𝛽a) was 0.013(1) GPa-1 in silicone-oil run, which is twice more compressible than the a(b)-axis in water and carbon dioxide runs, 𝛽a = 0.006(1) GPa-1. The bulk moduli were measured as 50(3) GPa, 52(3) GPa, and 29(2) GPa in water, carbon dioxide, and silicone-oil run, respectively. The orthorhombicities of ac-plane in the water, and carbon dioxide runs were comparatively constant, near 0.350~0.353, whereas the value decreased abruptly in the silicone-oil run following formula, y = -0.005(1)x + 0.351(1) by non-penetrating pressure fluid condition.

Sintering and Electrical Properties According to Sb/Bi Ratio(I) : ZnO-Bi2O3-Sb2O3-Mn3O4-Cr2O3 Varistor (Sb/Bi비에 따른 5원계 바리스터의 소결거동 및 전기적 특성(I) : ZnO-Bi2O3-Sb2O3-Mn3O4-Cr2O3)

  • Hong, Youn-Woo;Lee, Young-Jin;Kim, Sei-Ki;Kim, Jin-Ho
    • Korean Journal of Materials Research
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    • v.22 no.12
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    • pp.675-681
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    • 2012
  • We aimed to examine the co-doping effects of 1/6 mol% $Mn_3O_4$ and 1/4 mol% $Cr_2O_3$ (Mn:Cr = 1:1) on the reaction, microstructure, and electrical properties, such as the bulk defects and grain boundary properties, of ZnO-$Bi_2O_3-Sb_2O_3$ (ZBS; Sb/Bi = 0.5, 1.0, and 2.0) varistors. The sintering and electrical properties of Mn,Cr-doped ZBS, ZBS(MnCr) varistors were controlled using the Sb/Bi ratio. Pyrochlore ($Zn_2Bi_3Sb_3O_{14}$), ${\alpha}$-spinel ($Zn_7Sb_2O_{12}$), and ${\delta}-Bi_2O_3$ (also ${\beta}-Bi_2O_3$ at Sb/Bi ${\leq}$ 1.0) were detected for all of the systems. Mn and Cr are involved in the development of each phase. Pyrochlore was decomposed and promoted densification at lower temperature on heating in Sb/Bi = 1.0 system by Mn rather than Cr doping. A more homogeneous microstructure was obtained in all systems affected by ${\alpha}$-spinel. In ZBS(MnCr), the varistor characteristics were improved dramatically (non-linear coefficient, ${\alpha}$ = 40~78), and seemed to form ${V_o}^{\cdot}$(0.33 eV) as a dominant defect. From impedance and modulus spectroscopy, the grain boundaries can be seen to have divided into two types, i.e. one is tentatively assigned to ZnO/$Bi_2O_3$ (Mn,Cr)/ZnO (0.64~1.1 eV) and the other is assigned to the ZnO/ZnO (1.0~1.3 eV) homojunction.

Effect of Sb/Bi Ratio on Sintering and Grain Boundary Properties of ZnO-Bi2O3-Sb2O3-NiO-Cr2O3 Varistor (Sb/Bi비가 ZnO-Bi2O3-Sb2O3-NiO-Cr2O3 바리스터의 소결과 입계 특성에 미치는 영향)

  • Hong, Youn-Woo;Lee, Young-Jin;Kim, Sei-Ki;Kim, Jin-Ho
    • Korean Journal of Materials Research
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    • v.22 no.12
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    • pp.689-695
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    • 2012
  • We have examined the co-doping effects of 1/2 mol% NiO and 1/4 mol% $Cr_2O_3$ (Ni:Cr = 1:1) on the reaction, microstructure, and electrical properties, such as the bulk defects and the grain boundary properties, of ZnO-$Bi_2O_3-Sb_2O_3$ (ZBS; Sb/Bi = 0.5, 1.0, and 2.0) varistors. The sintering and electrical properties of Ni,Cr-doped ZBS, ZBS(NiCr) varistors were controlled using the Sb/Bi ratio. Pyrochlore ($Zn_2Bi_3Sb_3O_{14}$), ${\alpha}$-spinel ($Zn_7Sb_2O_{12}$), and ${\delta}-Bi_2O_3$ were detected for all of compositions. For the sample with Sb/Bi = 1.0, the Pyrochlore was decomposed and promoted densification at lower temperature by Ni rather than by Cr. A homogeneous microstructure was obtained for all of the samples affected by ${\alpha}$-spinel. The varistor characteristics were not dramatically improved (non-linear coefficient, ${\alpha}$ = 5~24), and seemed to form ${Zn_i}^{{\cdot}{\cdot}}$(0.17 eV) and ${V_o}^{\cdot}$(0.33 eV) as dominant defects. From impedance and modulus spectroscopy, the grain boundaries were found to have been divided into two types, i.e., one is tentatively assigned to ZnO/$Bi_2O_3$ (Ni,Cr)/ZnO (0.98 eV) and the other is assigned to a ZnO/ZnO (~1.5 eV) homojunction.

Sintering and Electrical Properties According to Sb/Bi Ratio(II) : ZnO-Bi2O3-Sb2O3-Co3O4-Cr2O3 Varistor (Sb/Bi비에 따른 5원계 바리스터의 소결거동 및 전기적 특성(II) : ZnO-Bi2O3-Sb2O3-Co3O4-Cr2O3)

  • Hong, Youn-Woo;Lee, Young-Jin;Kim, Sei-Ki;Kim, Jin-Ho
    • Korean Journal of Materials Research
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    • v.22 no.12
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    • pp.682-688
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    • 2012
  • In this study we aimed to examine the co-doping effects of 1/6 mol% $Co_3O_4$ and 1/4 mol% $Cr_2O_3$ (Co:Cr = 1:1) on the reaction, microstructure, and electrical properties, such as the bulk defects and the grain boundary properties, of ZnO-$Bi_2O_3-Sb_2O_3$ (ZBS; Sb/Bi = 0.5, 1.0, and 2.0) varistors. The sintering and electrical properties of Co,Cr-doped ZBS, ZBS(CoCr) varistors were controlled using the Sb/Bi ratio. Pyrochlore ($Zn_2Bi_3Sb_3O_{14}$), ${\alpha}$-spinel ($Zn_7Sb_2O_{12}$), and ${\delta}-Bi_2O_3$ were formed in all systems. Pyrochlore was decomposed and promoted densification at lower temperature on heating in Sb/Bi = 1.0 by Cr rather than Co. A more homogeneous microstructure was obtained in all systems affected by ${\alpha}$-spinel. In ZBS(CoCr), the varistor characteristics were improved (non-linear coefficient, ${\alpha}$ = 20~63), and seemed to form ${Zn_i}^{{\cdot}{\cdot}}$(0.20 eV) and ${V_o}^{\cdot}$(0.33 eV) as dominant defects. From impedance and modulus spectroscopy, the grain boundaries were found to be composed of an electrically single barrier (0.94~1.1 eV) that is, however, somewhat sensitive to ambient oxygen with temperature. The phase development, densification, and microstructure were controlled by Cr rather than by Co but the electrical and grain boundary properties were controlled by Co rather than by Cr.

Sintering and Electrical Properties of Cr-doped ZnO-Bi2O3-Sb2O3 (Cr을 첨가한 ZnO-Bi2O3-Sb2O3계의 소결과 전기적 특성)

  • Hong, Youn-Woo;Shin, Hyo-Soon;Yeo, Dong-Hun;Kim, Jin-Ho
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.23 no.12
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    • pp.942-948
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    • 2010
  • In this study we aims to examine the effects of 0.5 mol% $Cr_2O_3$ addition on the reaction, microstructure development, resultant electrical properties, and especially the bulk trap and interface state levels of ZnO-$Bi_2O_3-Sb_2O_3$ (Sb/Bi=0.5, 1.0, and 2.0) systems (ZBS). The samples were prepared by conventional ceramic process, and characterized by XRD, density, SEM, I-V, impedance and modulus spectroscopy (IS & MS) measurement. The sintering and electrical properties of Cr-doped ZBS (ZBSCr) systems were controlled by Sb/Bi ratio. Pyrochlore ($Zn_2Bi_3Sb_3O_{14}$) was decomposed more than $100^{\circ}C$ lowered on heating in ZBS (Sb/Bi=1.0) by Cr doping. The densification of ZBSCr (Sb/Bi=0.5) system was retarded to $800^{\circ}C$ by unknown Bi-rich phase produced at $700^{\circ}C$. Pyrochlore on cooling was reproduced in all systems. And $Zn_7Sb_2O_{12}$ spinel ($\alpha$-polymorph) and $\delta-Bi_2O_3$ phase were formed by Cr doping. In ZBSCr, the varistor characteristics were not improved drastically (non-linear coefficient $\alpha$ = 7~12) and independent on microstructure according to Sb/Bi ratio. Doping of $Cr_2O_3$ to ZBS seemed to form $Zn_i^{..}$(0.16 eV) and $V^{\bullet}_o$ (0.33 eV) as dominant defects. From IS & MS, especially the grain boundaries of Sb/Bi=0.5 systems were divided into two types, i.e. sensitive to oxygen and thus electrically active one (1.1 eV) and electrically inactive intergranular one (0.95 eV) with temperature.

Characteristics of Sand-Rubber Mixtures under Different Strain Levels: Experimental Observation (변형률에 따른 모래-고무 혼합재의 거동 특성: 실험적 관찰)

  • Lee, Chang-Ho;Byun, Yong-Hoon;Lee, Jong-Sub
    • Journal of the Korean Geotechnical Society
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    • v.27 no.3
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    • pp.85-94
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    • 2011
  • Mixtures of sand and rubber particles ($D_{sand}/D_{rubber}=1$) are investigated to explore their characteristics under different stain level. Mixtures are prepared with different volumetric sand fractions ($sf=V_{sand}/V_{total}$). Experimental data are gathered from a resonant column, an instrumented oedometer, and a direct shear tests. Results show that sand and rubber differently control the behavior of the whole mixture with strain level. Non-linear degradation of small strain stiffness is observed for the mixtures with $sf{\geq}0.4$, while the mixtures with low sand fraction ($sf{\leq}0.2$) show significantly high elastic threshold strain. Vertical stress-deformation increases dramatically when the rubber particle works as a member of force chain. The strength of the mixtures increases as the content of rubber particle decreases, and contractive behavior is observed in the mixtures with $sf{\leq}0.8$. Rubber particle plays different roles with strain level in the mixture: it increases a coordination number and controls a plasticity of the mixture in small strain; it prevents a buckling of force chain in intermediate strain; it leads a contractive behavior in large strain.

Effect of Sb/Bi Ratio on Sintering and Grain Boundary Properties of ZnO-Bi2O3-Sb2O3-Mn3O4-Co3O4 Varistor (Sb/Bi비가 ZnO-Bi2O3-Sb2O3-Mn3O4-Co3O4 바리스터의 소결과 입계 특성에 미치는 영향)

  • Hong, Youn-Woo;Lee, Young-Jin;Kim, Sei-Ki;Kim, Jin-Ho
    • Journal of the Korean Institute of Electrical and Electronic Material Engineers
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    • v.25 no.11
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    • pp.878-885
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    • 2012
  • In this study we aims to examine the co-doping effects of 1/3 mol% $Mn_3O_4+Co_3O_4$ (1:1) on the reaction, microstructure, and electrical properties such as the bulk defects and grain boundary properties of $ZnO-Bi_2O_3-Sb_2O_3$ (ZBS; Sb/Bi=0.5, 1.0, and 2.0) varistors. The sintering and electrical properties of Mn,Co-doped ZBS, ZBS(MCo) varistors were controlled by Sb/Bi ratio. Pyrochlore ($Zn_2Bi_3Sb_3O_{14}$) was decomposed and promoted densification at lower temperature on heating in Sb/Bi=1.0 by Mn rather than Co. Pyrochlore on cooling was reproduced in all systems however, spinel (${\alpha}$- or ${\beta}$-polymorph) did not formed in Sb/Bi=0.5. More homogeneous microstructure was obtained in $Sb/Bi{\geq}1.0$ In ZBS(MCo), the varistor characteristics were improved drastically (non-linear coefficient, ${\alpha}$=30~49), and seemed to form $Zn_i^{..}$(0.17 eV) and $V_o^{\bullet}$(0.33 eV) as dominant defects. From impedance and modulus spectroscopy (IS & MS), the grain boundaries have divided into two types, i.e. the one is tentatively assign to $ZnO/Bi_2O_3(Mn,Co)/ZnO$ (0.47 eV) and the other ZnO/ZnO (0.80~0.89 eV) homojunctions.