• Steel and Composite Structures
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• v.20 no.2
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• pp.227-249
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• 2016

The objective of this work is to present a zeroth-order shear deformation theory for free vibration analysis of functionally graded (FG) nanoscale plates resting on elastic foundation. The model takes into consideration the influences of small scale and the parabolic variation of the transverse shear strains across the thickness of the nanoscale plate and thus, it avoids the employ use of shear correction factors. Also, in this present theory, the effect of transverse shear deformation is included in the axial displacements by using the shear forces instead of rotational displacements as in available high order plate theories. The material properties are supposed to be graded only in the thickness direction and the effective properties for the FG nanoscale plate are calculated by considering Mori-Tanaka homogenization scheme. The equations of motion are obtained using the nonlocal differential constitutive expressions of Eringen in conjunction with the zeroth-order shear deformation theory via Hamilton's principle. Numerical results for vibration of FG nanoscale plates resting on elastic foundations are presented and compared with the existing solutions. The influences of small scale, shear deformation, gradient index, Winkler modulus parameter and Pasternak shear modulus parameter on the vibration responses of the FG nanoscale plates are investigated.

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09a
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• pp.289-290
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• 2006

[ $SrTiO_3$ ] is usually added as shifters in order to move the $T_C$ of $BaTiO_3$ to lower temperatures because it is well established that the $T_C$ of $BaTiO_3$ decreases linearly with a solid solution of $Sr^{+2}$ in place of $Ba^{+2}$. It is not fully understood yet, however, how $SrTiO_3$ influences on the peak value of the dielectric constant $(\varepsilon_{max})$ at the $T_C$ of $BaTiO_3$. This research reports the effect of $SrTiO_3$ addition on εmax at the $T_C$ of $BaTiO_3$ ceramics. Based on the chemical composition and the grain size dependence of the dielectric property of $BaTiO_3$ ceramics, functionally graded $(Ba,Sr)TiO_3$ composites were designed and fabricated. Multi-layered $(Ba,Sr)TiO_3$ composites with a compositional gradient of $SrTiO_3$ exhibited a low temperature coefficient and high dielectric constant in a wide temperature range.

• Structural Engineering and Mechanics
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• v.85 no.3
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• pp.289-304
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• 2023

The main objective of this paper is to study the effect of porosity on the buckling behavior of thick functionally graded sandwich plate resting on various boundary conditions under different in-plane loads. The formulation is made for a newly developed sandwich plate using a functional gradient material based on a modified power law function of symmetric and asymmetric configuration. Four different porosity distribution are considered and varied in accordance with material propriety variation in the thickness direction of the face sheets of sandwich plate, metal foam also is considered in this study on the second model of sandwich which containing metal foam core and FGM face sheets. New quasi-3D high shear deformation theory is used here for this investigate; the present kinematic model introduces only six variables with stretching effect by adopting a new indeterminate integral variable in the displacement field. The stability equations are obtained by Hamilton's principle then solved by generalized solution. The effect of Pasternak and Winkler elastic foundations also including here. the present model validated with those found in the open literature, then the impact of different parameters: porosities index, foam cells distribution, boundary conditions, elastic foundation, power law index, ratio aspect, side-to-thickness ratio and different in-plane axial loads on the variation of the buckling behavior are demonstrated.

• Korean Journal of Materials Research
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• v.3 no.3
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• pp.261-271
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• 1993

Functionally Gradient Materials(FGM) of 4.5Pb($Ni_{1/3}Nb_{2/3})O_3$-55PZT and PLZT(lO/70 /30, 11/60/40) were prepared. Its dielectric and piezoelectric strain properties were investigated. The FGM were pressed into A/B/ A configuration using two kinds of films, one layer(A) was eliminated from FGM by polishing after sintering at $l250^{\circ}C$, 2 hrs. The acrylic binder system was successfully applied for crack free film through doctor blade method. The thickness of gradent layer in FGM was about 30${\mu}$m. Dielectric properties of FGM show the average value of each side layer. The strain-electric field characteristics of FGM were significantly improved comparison with the other single compositions. The prepared FGM piezoelectric actuator shows about 3${\mu}$m/IOOV displacement.

• Structural Engineering and Mechanics
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• v.64 no.1
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• pp.121-133
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• 2017

This paper proposes an analytical solution method for free vibration of curved functionally graded (FG) nonlocal beam supposed to different thermal loadings, by considering porosity distribution via nonlocal elasticity theory for the first time. Material properties of curved FG beam are assumed to be temperature-dependent. Thermo-mechanical properties of porous FG curved beam are supposed to vary through the thickness direction of beam and are assumed to be temperature-dependent. Since variation of pores along the thickness direction influences the mechanical and physical properties, porosity play a key role in the mechanical response of curved FG structures. The rule of power-law is modified to consider influence of porosity according to even distribution. The governing equations of curved FG porous nanobeam under temperature field are derived via the energy method based on Timoshenko beam theory. An analytical Navier solution procedure is used to achieve the natural frequencies of porous FG curved nanobeam supposed to thermal loadings with simply supported boundary condition. The results for simpler states are confirmed with known data in the literature. The effects of various parameters such as nonlocality, porosity volume fractions, type of temperature rising, gradient index, opening angle and aspect ratio of curved FG porous nanobeam on the natural frequency are successfully discussed. It is concluded that these parameters play key roles on the dynamic behavior of porous FG curved nanobeam. Presented numerical results can serve as benchmarks for future analyses of curve FG nanobeam with porosity phases.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2004.07b
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• pp.802-805
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• 2004

압전 액츄에이터는 다른 종류의 액츄에이터와 비교할 때 높은 강성, 빠른 응답성의 우수한 특성을 가지고 있다. 벤더형 액츄에이터는 높은 변위의 장점을 가지나 높은 전기장과 기계적 부하인가시에는 내부 응력이 증가하므로서 신뢰성이 감소한다는 단점을 가지고 있다. 이러한 단점을 보완하기 위하여 여러 방법으로 내부 응력을 줄이려는 시도가 있으며 그중 하나는 경사기능 소재나 경사기능 구조를 가지는 액츄에이터의 개발이다. 본 연구에서는 경사기능 특성을 모사한 액츄에이터 구조를 제작하고 그 특성을 조사하였다. 두 가지의 압전상수 d31= - 220 pC/N, d31 =- 100 pC/N를 가지는 세라믹층을 적층하여 벤더형 액츄에이터의 특성을 관찰하였다. 그 결과 두 종류의 세라믹층으로 적층한 액츄에이터가 한가지 특성의 세라믹으로 제작한 액츄에이터 보다 전압인가시 20%이상의 우수한 변위 특성을 나타내었다. 이러한 변화는 내부 응력의 감소에 기인한 것으로 예상된다.

• Steel and Composite Structures
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• v.49 no.6
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• pp.603-614
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• 2023

In this paper, frequency analysis of curved functionally graded (FG) nanobeam by consideration of deepness effect has been studied. Differential transform method (DTM) has been used to obtain frequency responses. The nonlocal theory of Eringen has been applied to consider nanoscales. Material properties are supposed to vary in radial direction according to power-law distribution. Differential equations and related boundary conditions have been derived using Hamilton's principle. Finally, by consideration of nonlocal theory, the governing equations have been derived. Natural frequencies have been obtained using semi analytical method (DTM) for different boundary conditions. In order to study the effect of deepness, the deepness term is considered in strain field. The effects of the gradient index, radius of curvature, the aspect ratio, the nonlocal parameter and interaction of aforementioned parameters on frequency value for different boundary conditions such as clamped-clamped (C-C), clamped-hinged (C-H), and clamped-free (C-F) have been investigated. In addition, the obtained results are compared with the results in previous literature in order to validate present study, a good agreement was observed in the present results.

• Advances in nano research
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• v.17 no.1
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• pp.9-18
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• 2024

This paper presents the development of an educational management model for analyzing the dynamic instability of nanocomposite sandwich beams. The model aims to provide a comprehensive framework for understanding the behavior of sandwich micro beams with foam cores, featuring top and bottom layers made of smart and porous functionally graded materials (FGM) nanocomposites. The bottom layer is influenced by an external electric field, and the entire beam is supported by a visco-Pasternak foundation, accounting for spring, shear, and damping constants. Using the Kelvin-Voigt theory to model structural damping and incorporating size effects based on strain gradient theory, the model employs the parabolic shear deformation beam theory (PSDBT) to derive motion equations through Hamilton's principle. The differential quadrature method (DQM) is applied to solve these equations, accurately identifying the improvement in student understanding (ISU) of the beams. The impact of various parameters, including FGM properties, external voltage, geometric constants, and structural damping, on the DIR is thoroughly examined. The educational model is validated by comparing its outcomes with existing studies, highlighting the increase in ISU with the application of negative external voltage to the smart layer. This model serves as a valuable educational tool for engineering students and researchers studying the dynamic stability of advanced nanocomposite structures.

• Steel and Composite Structures
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• v.21 no.1
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• pp.1-36
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• 2016

In the present study, the nonlinear magneto-electro-mechanical free vibration behavior of rectangular double-bonded sandwich microbeams based on the modified strain gradient theory (MSGT) is investigated. It is noted that the top and bottom sandwich microbeams are considered with boron nitride nanotube reinforced composite face sheets (BNNTRC-SB) with electrical properties and carbon nanotube reinforced composite face sheets (CNTRC-SB) with magnetic fields, respectively, and also the homogenous core is used for both sandwich beams. The connections of every sandwich beam with its surrounding medium and also between them have been carried out by considering Pasternak foundations. To take size effect into account, the MSGT is introduced into the classical Timoshenko beam theory (CT) to develop a size-dependent beam model containing three additional material length scale parameters. For the CNTRC and BNNTRC face sheets of sandwich microbeams, uniform distribution (UD) and functionally graded (FG) distribution patterns of CNTs or BNNTs in four cases FG-X, FG-O, FG-A, and FG-V are employed. It is assumed that the material properties of face sheets for both sandwich beams are varied in the thickness direction and estimated through the extended rule of mixture. On the basis of the Hamilton's principle, the size-dependent nonlinear governing differential equations of motion and associated boundary conditions are derived and then discretized by using generalized differential quadrature method (GDQM). A detailed parametric study is presented to indicate the influences of electric and magnetic fields, slenderness ratio, thickness ratio of both sandwich microbeams, thickness ratio of every sandwich microbeam, dimensionless three material length scale parameters, Winkler spring modulus and various distribution types of face sheets on the first two natural frequencies of double-bonded sandwich microbeams. Furthermore, a comparison between the various beam models on the basis of the CT, modified couple stress theory (MCST), and MSGT is performed. It is illustrated that the thickness ratio of sandwich microbeams plays an important role in the vibrational behavior of the double-bonded sandwich microstructures. Meanwhile, it is concluded that by increasing H/lm, the values of first two natural frequencies tend to decrease for all amounts of the Winkler spring modulus.

• Composites Research
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• v.16 no.3
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• pp.68-74
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• 2003

In this paper, intermetallic/metal laminated composites have been successfully produced that utilizes SHS reactions between Ni and Al elemental metal foils. The reaction between Ni and Al started from the nucleation and growth of NiA1$_3$ and was followed by the diffusional growth of Ni$_2$A1$_3$ between Ni and NiA1$_3$. The SHS reaction was thermodynamically analyzed through the final volume fraction of the non-reacted Al related with the initial thickness ratio of Ni:Al and prior heat treatment. Thermally aging these 1aminates resulted in formation of a functionally gradient series of intermetallic phases. Microstructure showed that the intermetallic volume percent was 82, 59.5, 40% in the 1:1, 2:1, 4:1 thickness ratio specimen. Main phases of the intermetallic were NiAl and Ni$_3$Al having higher strength at room and high temperatures.