• Advances in nano research
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• v.9 no.4
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• pp.295-307
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• 2020

The vibrational characteristics of Multi-Phase Nanocomposite (MPC) reinforced annular/circular plate under initially stresses are presented using the state-space formulation based on three-dimensional elasticity theory (3D-elasticity theory) and Differential Quadrature Method (DQM). The MPC reinforced annular/circular plate is under initial lateral stress and composed of multilayers with Carbon Nanotubes (CNTs) uniformly dispersed in each layer, but its properties change layer-by-layer along the thickness direction. The State-Space based Differential Quadrature Method (SS-DQM) is presented to examine the frequency behavior of the current structure. Halpin-Tsai equations and fiber micromechanics are used in the hierarchy to predict the bulk material properties of the multi-scale composite. A singular point is investigated for modeling the circular plate. The CNTs are supposed to be randomly oriented and uniformly distributed through the matrix of epoxy resin. Afterward, a parametric study is done to present the effects of various types of sandwich circular/annular plates on frequency characteristics of the MPC reinforced annular/circular plate using 3D-elasticity theory.

• Advances in nano research
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• v.8 no.1
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• pp.69-82
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• 2020

In this study, the free and forced vibration analysis of micro sandwich plate with porous core layer and magneto-electric face sheets based on modified couple stress theory and first order shear deformation theory under simply supported boundary conditions is illustrated. It is noted that the core layer is composed from balsa wood and also piezo magneto-electric facesheets are made of BiTiO₃-CoFe₂O₄. Using Hamilton's principle, the equations of motion for micro sandwich plate are obtained. Also, the Navier's method for simply support boundary condition is used to solve these equations. The effects of applied voltage, magnetic field, length to width ratio, thickness of porous to micro plate thickness ratio, type of porous, coefficient of porous on the frequency ratio are investigated. The numerical results indicate that with increasing of the porous coefficient, the non-dimensional frequency increases. Also, with an increase in the electric potential, the non-dimensional frequency decreases, while and with increasing of the magnetic potential is vice versa.

• Advances in nano research
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• v.7 no.2
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• pp.109-123
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• 2019

In this article, the free vibration analysis of annular sandwich plates with various functionally graded (FG) porous cores and carbon nanotubes reinforced composite (CNTRC) facesheets is investigated based on modified couple stress theory (MCST) and first order shear deformation theories (FSDT). The annular sandwich plate is composed of two face layers and a functionally graded porous core layer which contains different porosity distributions. Various approaches such as extended mixture rule (EMR), Eshelby-Mori-Tanaka (E-M-T), and Halpin-Tsai (H-T) are used to determine the effective material properties of microcomposite circular sandwich plate. The governing equations of motion are extracted by using Hamilton's principle and FSDT. A Ritz method has been utilized to calculate the natural frequency of an annular sandwich plate. The effects of material length scale parameters, boundary conditions, aspect and inner-outer radius ratios, FG porous distributions, pore compressibility and volume fractions of CNTs are considered. The results are obtained by Ritz solutions that can be served as benchmark data to validate their numerical and analytical methods in the future work and also in solid-state physics, materials science, and micro-electro-mechanical devices.

• Advances in nano research
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• v.16 no.1
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• pp.27-40
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• 2024

This work is the first of its kind to integrate Mindlin's theory with analytical methods in order to produce an exact solution to a specific vibration issue as well as a bending problem involving a nanoplate that is supported by a viscoelastic foundation. The plate is exposed to the simultaneous effects of a compressive load in the plate plane and a force operating perpendicular to the plane of the nanoplate. In addition, the flexoelecity effect is included into the plate. The strain gradient component is taken into consideration while calculating the plate equilibrium equation using the nonlocal theory and Hamilton's principle. The free vibration and static responses of the nanoplate seem to be both real and imaginary components because of the appearance of the viscoelastic drag coefficient of the viscoelastic foundation. This study also shows that when analyzing the mechanical response for nanostructure, taking into account the flexoelectricity effect and the influence of the nonlocal parameter, the results will be completely different from the case in which this parameter is ignored. This indicates that it is vital to take into consideration the effects of nonlocal parameters on the nanosheet structure while also taking into consideration the effect of flexoelectricity.

• Advances in aircraft and spacecraft science
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• v.5 no.6
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• pp.691-729
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• 2018

In this paper the hygro-thermo-mechanical vibration and buckling behavior of embedded FG nano-plates are investigated. The Eringen's and Gurtin-Murdoch theories are applied to study the small scale and surface effects on frequencies and critical buckling loads. The effective material properties are modeled using Mori-Tanaka homogenization scheme. On the base of RPT and HSDPT plate theories, the Hamilton's principle is employed to derive governing equations. Using iterative and GDQ methods the governing equations are solved and the influence of different parameters on natural frequencies and critical buckling loads are studied.

• Structural Monitoring and Maintenance
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• v.7 no.1
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• pp.27-42
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• 2020

Dynamic stability of graded nonlocal nano-dimension plates on elastic substrate due to in-plane periodic loads has been researched via a novel 3- unknown plate theory based on exact position of neutral surface. Proposed theory confirms the shear deformation effects and contains lower field components in comparison to first order and refined 4- unknown plate theories. A modified power-law function has been utilized in order to express the porosity-dependent material coefficients. The equations of nanoplate have been represented in the context of Mathieu-Hill equations and Chebyshev-Ritz-Bolotin's approach has been performed to derive the stability boundaries. Detailed impacts of static/dynamic loading parameters, nonlocal constant, foundation parameters, material index and porosities on instability boundaries of graded nanoscale plates are researched.

• Structural Engineering and Mechanics
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• v.76 no.1
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• pp.27-56
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• 2020

In this paper, the deflection and buckling analyses of porous nano-composite piezoelectric plate reinforced by carbon nanotube (CNT) are studied. The equations of equilibrium using energy method are derived from principle of minimum total potential energy. In the research, the non-local strain gradient theory is employed to consider size dependent effect for porous nanocomposite piezoelectric plate. The effects of material length scale parameter, Eringen's nonlocal parameter, porosity coefficient and aspect ratio on the deflection and critical buckling load are investigated. The results indicate that the effect of porosity coefficient on the increase of the deflection and critical buckling load is greatly higher than the other parameters effect, and size effect including nonlocal parameter and the material length scale parameter have a lower effect on the deflection increase with respect to the porosity coefficient, respectively and vice versa for critical buckling load. Porous nanocomposites are used in various engineering fields such as aerospace, medical industries and water refinery.

• Steel and Composite Structures
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• v.36 no.1
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• pp.87-101
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• 2020

A multi-scale epoxy/CNT/fiberglass annular sector plate is studied in this paper in the view of determining nonlinear forced vibration characteristics. A 3D Mori-Tanaka model is employed for evaluating multi-scale material properties. Thus, all of glass fibers are assumed to have uni-direction alignment and CNTs have random diffusion. The geometry of annular sector plate can be described based on the open angle and the value of inner/outer radius. In order to solve governing equations and derive exact forced vibration curves for the multi-scale annular sector, Jacobi elliptic functions are used. Obtained results demonstrate the significance of CNT distribution, geometric nonlinearity, applied force, fiberglass volume, open angle and fiber directions on forced vibration characteristics of multi-scale annular sector plates.

• Advances in nano research
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• v.7 no.1
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• pp.63-75
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• 2019

This article represents a quasi-3D theory for the buckling investigation of magneto-electro-elastic functionally graded (MEE-FG) nanoplates. All the effects of shear deformation and thickness stretching are considered within the presented theory. Magneto-electro-elastic material properties are considered to be graded in thickness direction employing power-law distribution. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of such nanoplates. Using Hamilton's principle, the nonlocal governing equations based on quasi-3D plate theory are obtained for the buckling analysis of MEE-FG nanoplates including size effect and they are solved applying analytical solution. It is found that magnetic potential, electric voltage, boundary conditions, nonlocal parameter, power-law index and plate geometrical parameters have significant effects on critical buckling loads of MEE-FG nanoscale plates.

• Smart Structures and Systems
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• v.23 no.5
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• pp.429-447
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• 2019

The present study analyzed free vibration of the three-layered micro annular/circular plate which its core and face sheets are made of saturated porous materials and FG-CNTRCs, respectively. The structure is subjected to magneto-electric fields and magneto-electro-mechanical pre loads. Mechanical properties of the porous core and also FG-CNTRC face sheets are varied through the thickness direction. Using dynamic Hamilton's principle, the motion equations based on MCS and FSD theories are derived and solved via GDQ as an efficient numerical method. Effect of different parameters such as pores distributions, porosity coefficient, pores compressibility, CNTs distribution, elastic foundation, multi-physical pre loads, small scale parameter and aspect ratio of the plate are investigated. The findings of this study can be useful for designing smart structures such as sensor and actuator.