• Smart Structures and Systems
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• 제20권5호
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• pp.573-581
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• 2017

A vibrating double-layered nanoscale piezoelectric plate is developed accounting for the flexoelectricity and surface effects. The flexoelectricity is due to the coupling between electrical polarization and strain gradient. Applying Hamilton's principle, the governing equations and related boundary conditions are derived. Assuming suitable approximate functions, the governing equations are numerically solved for simply-supported and clamped boundary conditions. Obtained results indicate that both the flexoelectricity and surface effects possess notable impact on the vibration frequencies of the system. Only flexoelectricity yields a considerable difference between the present model and previous investigations on conventional piezoelectric nanoplates. Generally, a parametric study has been performed to examine the effects of surface elasticity, flexoelectricity, applied electric voltage, interlayer stiffness, geometrical parameters and boundary conditions on vibration frequencies of piezoelectric nanoplates.

• Structural Engineering and Mechanics
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• 제67권2호
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• pp.143-153
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• 2018

Thermal buckling of nonlocal flexoelectric nanoplates incorporating surface effects is analyzed for the first time. Coupling of strain gradients and electrical polarizations is introduced by flexoelectricity. It is assumed that flexoelectric nanoplate is subjected to uniform and linear temperature distributions. Long range interaction between atoms of nanoplate is modeled via nonlocal elasticity theory. The residual surface stresses which are usually neglected in modeling of flexoelectric nanoplates are incorporated into nonlocal elasticity to provide better understanding of the physic of problem. A Galerkin-based approach is implemented to solve the governing equations derived from Hamilton's principle are solved. The verification of obtained results is performed by comparing buckling loads of flexoelectric nanoplate with previous data. It is shown that buckling loads of flexoelectric nanoplate are significantly affected by thermal loading type, temperature change, nonlocal parameter, surface effect, plate thickness and boundary conditions.

• Advances in nano research
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• 제5권4호
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• pp.393-414
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• 2017

Forced vibration behavior of porous metal foam nanoplates on elastic medium is studied via a 4-variable plate theory. Different porosity distributions called uniform, symmetric and asymmetric are considered. Nonlocal strain gradient theory (NSGT) containing two scale parameters is employed for size-dependent modeling of porous nanoplates. The present plate theory satisfies the shear deformation effect and it has lower field variables compared with first order plate theory. Hamilton's principle is employed to derive the governing equations. Obtained results from Galerkin's method are verified with those provided in the literature. The effects of nonlocal parameter, strain gradient, foundation parameters, dynamic loading, porosity distributions and porosity coefficient on dynamic deflection and resonance frequencies of metal foam nanoscale plates are examined.

• Steel and Composite Structures
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• 제32권2호
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• pp.281-292
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• 2019

Nonlocal elasticity and Reddy plant theory are used to study the vibration response of functionally graded (FG) nanoplates resting on two parameters elastic medium called Pasternak foundation. Nonlocal higher order theory accounts for the effects of both scale and the effect of transverse shear deformation, which becomes significant where stocky and short nanoplates are concerned. It is assumed that the properties of FG nanoplate follow a power law through the thickness. In addition, Poisson's ratio is assumed to be constant in this model. Both Winkler-type and Pasternak-type foundation models are employed to simulate the interaction of nanoplate with surrounding elastic medium. Using Hamilton's principle, size-dependent governing differential equations of motion and corresponding boundary conditions are derived. A differential quadrature approach is being utilized to discretize the model and obtain numerical solutions for various boundary conditions. The model is validated by comparing the results with other published results.

• Structural Engineering and Mechanics
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• 제82권6호
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• pp.701-711
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• 2022

The nonlocal elasticity as well as Mindlin's first-order shear deformation plate theory are proposed to investigate thermal vibrational of a nanoplate placing on a three-factor foundation. The Winkler-Pasternak elastic foundation is connected with the viscous damping to obtain the present three-parameter viscoelastic model. Differential equations of motion are derived and resolved for simply-supported nanoplates to get their natural frequencies. The influences of the nonlocal index, viscous damping index, and temperature changes are investigated. A comparison example is dictated to validate the precision of present results. Effects of other factors such as aspect ratio, mode numbers, and foundation parameters are discussed carefully for the vibration problem. Additional thermal vibration results of nanoplates resting on the viscoelastic foundation are presented for comparisons with future investigations.

• Structural Engineering and Mechanics
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• 제73권2호
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• pp.191-207
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• 2020

This study aims at investigating the size-dependent free vibration of porous nanoplates when exposed to hygrothermal environment and rested on Kerr foundation. Based on the modified power-law model, material properties of porous functionally graded (FG) nanoplates are supposed to change continuously along the thickness direction. The generalized nonlocal strain gradient elasticity theory incorporating three scale factors (i.e. lower- and higher-order nonlocal parameters, strain gradient length scale parameter), is employed to expand the assumption of second shear deformation theory (SSDT) for considering the small size effect on plates. The governing equations are obtained based on Hamilton's principle and then the equations are solved using an analytical method. The elastic Kerr foundation, as a highly effected foundation type, is adopted to capture the foundation effects. Three different patterns of porosity (namely, even, uneven and logarithmic-uneven porosities) are also considered to fill some gaps of porosity impact. A comparative study is given by using various structural models to show the effect of material composition, porosity distribution, temperature and moisture differences, size dependency and elastic Kerr foundation on the size-dependent free vibration of porous nanoplates. Results show a significant change in higher-order frequencies due to small scale parameters, which could be due to the size effect mechanisms. Furthermore, Porosities inside of the material properties often present a stiffness softening effect on the vibration frequency of FG nanoplates.

• 대한화학회지
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• 제59권2호
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• pp.148-155
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• 2015

결정핵-매개 소프트-용액 방법을 이용하여 판상형 ZnO 나노입자를 합성하였다. 합성된 판상형 ZnO 나노입자는 많은 결함이 존재하는 (0001)면이 발달하여 상업적인 ZnO 나노입자 보다 광촉매 특성이 우수하였다. 또한, 판상형 ZnO 나노입자의 세포독성이 실리카 코팅을 통해 감소함을 확인하였다. 마지막으로 판상형 ZnO를 합성하는데 필요한 성장용액의 다양한 시약 조건들을 변화시키면서 상업적인 적용이 가능한 수백 그램 스케일로 대량합성 하는데 처음으로 성공하였다.

• Steel and Composite Structures
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• 제52권3호
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• pp.273-291
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• 2024

This paper presents a three-dimensional displacement-based formulation to investigate the free vibration of functionally graded nanoplates resting on a Winkler-Pasternak foundation based on the nonlocal elasticity theory. The material properties of the FG nanoplate are considered to vary continuously through the thickness of the nanoplate according to the power-law distribution model. A general three-dimensional displacement field is considered for the plate, which takes into account the out-of-plane strains of the plate as well as the in-plane strains. Unlike the shear deformation theories, in the present formulation, no predetermined form for the distribution of displacements and transverse strains is considered. The equations of motion for functionally graded nanoplate are derived based on Hamilton's principle. The solution is obtained for simply-supported nanoplate, and the predicted results for natural frequencies are compared with the predictions of shear deformation theories which are available in the literature. The predictions of the present theory are discussed in detail to investigate the effects of power-law index, length-to-thickness ratio, mode numbers and the elastic foundation on the dynamic behavior of the functionally graded nanoplate. The present study presents a three-dimensional solution that is able to determine more accurate results in predicting of the natural frequencies of flexural and thickness modes of nanoplates. The effects of parameters that play a key role in the analysis and mechanical design of functionally graded nanoplates are investigated.

• Steel and Composite Structures
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• 제29권1호
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• pp.53-66
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• 2018

A high-order nonlocal strain gradient model is developed for wave propagation analysis of porous FG nanoplates resting on a gradient hybrid foundation in thermal environment, for the first time. Material properties are assumed to be temperature-dependent and graded in the nanoplate thickness direction. To consider the thermal effects, uniform, linear, nonlinear, exponential, and sinusoidal temperature distributions are considered for temperature-dependent FG material properties. On the basis of the refined-higher order shear deformation plate theory (R-HSDT) in conjunction with the bi-Helmholtz nonlocal strain gradient theory (B-H NSGT), Hamilton's principle is used to derive the equations of wave motion. Then the dispersion relation between frequency and wave number is solved analytically. The influences of various parameters (such as temperature rise, volume fraction index, porosity volume fraction, lower and higher order nonlocal parameters, material characteristic parameter, foundations components, and wave number) on the wave propagation behaviors of porous FG nanoplates are investigated in detail.

• Smart Structures and Systems
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• 제21권1호
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• pp.15-25
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• 2018

This work presents the buckling investigation of embedded orthotropic nanoplates such as graphene by employing a new refined plate theory and nonlocal small-scale effects. The elastic foundation is modeled as two-parameter Pasternak foundation. The proposed two-variable refined plate theory takes account of transverse shear influences and parabolic variation of the transverse shear strains within the thickness of the plate by introducing undetermined integral terms, hence it is unnecessary to use shear correction factors. Nonlocal governing equations for the single layered graphene sheet are obtained from the principle of virtual displacements. The proposed theory is compared with other plate theories. Analytical solutions for buckling loads are obtained for single-layered graphene sheets with isotropic and orthotropic properties. The results presented in this study may provide useful guidance for design of orthotropic graphene based nanodevices that make use of the buckling properties of orthotropic nanoplates.