• Steel and Composite Structures
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• 제34권2호
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• pp.215-226
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• 2020

The aim of this study is to investigate free vibration of functionally graded porous nanocomposite rectangular plates where the internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The GPL-reinforced plate is modeled using a semi-analytic approach composed of generalized differential quadrature method (GDQM) and series solution adopted to solve the equations of motion. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. New results reveal the importance of porosity coefficient, porosity distribution, graphene platelets (GPLs) distribution, geometrical and boundary conditions on vibration behavior of porous nanocomposite plates. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution.

• Steel and Composite Structures
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• 제37권6호
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• pp.711-731
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• 2020

This paper deals with free vibration of FG sandwich annular sector plates on Pasternak elastic foundation with different boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. The influence of carbon nanotubes (CNTs) waviness, aspect ratio, internal pores and graphene platelets (GPLs) on the vibrational behavior of functionally graded nanocomposite sandwich plates is investigated in this research work. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness of upper and bottom layers of the sandwich sectorial plates and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. The core of structure is porous and the internal pores and graphene platelets (GPLs) are distributed in the matrix of core either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. A semi-analytic approach composed of 2D-Generalized Differential Quadrature Method (2D-GDQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The new results can be used as benchmark solutions for future researches.

• Computers and Concrete
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• 제19권6호
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• pp.677-687
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• 2017

The nonlinear buckling response of nano composite anti-symmetric functionally graded polymeric microplate reinforced by single-walled carbon nanotubes (SWCNTs) rested on orthotropic elastomeric foundation with temperature dependent properties is investigated. For the carbon-nanotube reinforced composite (CNTRC) microplate, a uniform distribution (UD) and four types of functionally graded (FG) distribution are considered. Based on orthotropic Mindlin plate theory, von Karman geometric nonlinearity and Hamilton's principle, the governing equations are derived. Generalized differential quadrature method (GDQM) is employed to calculate the non-linear buckling response of the plate. Effects of FG distribution type, elastomeric foundation, aspect ratio (thickness to width ratio), boundary condition, orientation of foundation orthotropy and temperature are considered. The results are validated. It is found that the critical buckling load without elastic medium is significantly lower than considering Winkler and Pasternak medium.

• Smart Structures and Systems
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• 제17권5호
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• pp.837-857
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• 2016

In the present study, for first time the size dependent vibration behavior of a rotating functionally graded (FG) Timoshenko nanobeam based on Eringen's nonlocal theory is investigated. It is assumed that the physical and mechanical properties of the FG nanobeam are varying along the thickness based on a power law equation. The governing equations are determined using Hamilton's principle and the generalized differential quadrature method (GDQM) is used to obtain the results for cantilever boundary conditions. The accuracy and validity of the results are shown through several numerical examples. In order to display the influence of size effect on first three natural frequencies due to change of some important nanobeam parameters such as material length scale, angular velocity and gradient index of FG material, several diagrams and tables are presented. The results of this article can be used in designing and optimizing elastic and rotary type nano-electro-mechanical systems (NEMS) like nano-motors and nano-robots including rotating parts.

• Steel and Composite Structures
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• 제25권4호
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• pp.415-426
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• 2017

The thermo-mechanical vibration behavior of two dimensional functionally graded (2D-FG) porous nanobeam is reported in this paper. The material properties of the nanobeam are variable along thickness and length of the nanobeam according to the power law function. The nanobeam is modeled within the framework of Timoshenko beam theory. Eringen's nonlocal elasticity theory is used to develop the governing equations. Using the generalized differential quadrature method (GDQM) the governing equations are solved. The effect of porosity, temperature distribution, nonlocal value, L/h, FG power indexes along thickness and length and are investigated using parametric studies.

• Wind and Structures
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• 제24권3호
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• pp.267-285
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• 2017

This paper addresses vibration and instability of embedded functionally graded (FG)-carbon nanotubes (CNTs)-reinforced pipes conveying viscous fluid. The surrounding elastic medium is modeled by temperature-dependent orthotropic Pasternak medium. Flugge shell model is applied for mathematical modeling of structure. Based on energy method and Hamilton's principal, the motion equations are derived. Differential quadrature method (GDQM) is applied for obtaining the frequency and critical fluid velocity of system. The effects of different parameters such as volume percent of CNTs, elastic medium, boundary condition and geometrical parameters are discussed.

• Steel and Composite Structures
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• 제39권5호
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• pp.565-581
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• 2021

In this paper the buckling analysis of the nanoplate made of arbitrary bi-directional functionally graded (BDFG) materials with small scale effects are investigated. To study the small-scale effects on buckling load, the Eringen's nonlocal theory is applied. Employing the principle of minimum potential energy, the governing equations are obtained. Generalize differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the buckling load of BDFG nanoplates. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. Comparison between the results of GDQ method and other papers for buckling analysis of a simply supported rectangular nano FGM plate reveals the accuracy of GDQ method. At the end some numerical results are presented to study the effects of material length scale parameter, plate thickness, aspect ratio, Poisson's ratio boundary condition and side to thickness ratio on size dependent Frequency.

• Advances in nano research
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• 제10권1호
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• pp.1-14
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• 2021

In the present computational approach, thermal buckling and frequency characteristics of a doubly curved laminated nanopanel with the aid of Two-Dimensional Generalized Differential Quadrature Method (2D-GDQM) and Nonlocal Strain Gradient Theory (NSGT) are investigated. Additionally, the temperature changes along the thickness direction nonlinearly. The novelty of the current study is in considering the effects of laminated composite and thermal in addition of size effect on frequency, thermal buckling, and dynamic deflections of the laminated nanopanel. The acquired numerical and analytical results are compared by each other to validate the results. The results demonstrate that some geometrical and physical parameters, have noticeable effects on the frequency and pre-thermal buckling behavior of the doubly curved open cylindrical laminated nanopanel. The favorable suggestion of this survey is that for designing the laminated nano-sized structure should pay special attention to size-dependent parameters because nonlocal and length scale parameters have an important role in the static and dynamic behaviors of the laminated nanopanel.

• Computers and Concrete
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• 제30권3호
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• pp.185-196
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• 2022

In this paper, the dynamic characteristics of a composite cylindrical beam made of a mechanism of carbon dioxide absorption coated on the tube core are investigated based on the classical beam theory coupled with the modified couple stress theory. The composite tube structures are assumed to be uniform along the tube length, and the energy method regarding the Hamilton principle is utilized for generating the governing equations. A powerful numerical solution, the generalized differential quadrature method (GDQM), is employed to solve the differential equations. The carbon dioxide trapping mechanism is a composite consisting of a polyacrylonitrile substrate and a cross-link polydimethylsiloxane gutter layer. Methacrylate, poly (ethylene glycol), methyl ether methacrylate, and three pedant methacrylates are all taken into account as potential mechanisms for capturing carbon dioxide. The application of the present study is helpful in the design and production of microelectromechanical systems (MEMS) and the different valuable parameters, such as the length-scale parameter, rate of section change, aspect ratio, etc., are presented in detail.

• Advances in nano research
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• 제13권1호
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• pp.63-75
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• 2022

The nonlinear dynamic behavior of a nonuniform small-scale nonlocal beam is investigated in this work. The nanobeam is theoretically modeled using the nonlocal Eringen theory, as well as a few of Von-nonlinear Kármán's theories and the classical beam theory. The Hamilton principle extracts partial differential equations (PDE) of an axially functionally graded (AFG) nano-scale beam consisting of SUS304 and Si₃N₄ throughout its length, and an elastic Winkler-Pasternak substrate supports the tapered AFG nanobeam. The beam thickness is a function of beam length, and it constantly varies throughout the length of the beam. The numerical solution strategy employs an iteration methodology connected with the generalized differential quadratic method (GDQM) to calculate the nonlinear outcomes. The nonlinear numerical results are presented in detail to examine the impact of various parameters such as nonlinear amplitude, nonlocal parameter, the component of the elastic foundation, rate of cross-section change, and volume fraction parameter on the linear and nonlinear free vibration characteristics of AFG nanobeam.