• 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.

• Advances in nano research
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• 제12권6호
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• pp.567-581
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• 2022

The free and forced vibration in addition to electric energy harvesting of a piezoelectric disk resting on two-parameter foundation modeled by modified couple stress as well as Kirchhoff plate theory is probed. The governing equations and boundary conditions are obtained using Hamilton's principle. Then, the free and forced vibration are solved using numerical solutions, generalized differential quadrature method (GDQM) and Newmark-beta method. The forced vibration is resulted from a base excitation load. Also, the possible voltage which can be harvested from this system is obtained using generalized integral quadrature method. The validity of the formulation and solution procedure is confirmed using a compassion study. The impact of parameters such as length effect, inner to outer radius ratio, and foundations parameters on the free and forced vibration as well as energy harvesting is investigated in detail. This paper can be a basis for future studies in the area of piezoelectric harvesters in small scales.

• Advances in aircraft and spacecraft science
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• 제3권4호
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• pp.379-397
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• 2016

In this manuscript, free vibrations of a unidirectional composite orthotropic Timoshenko beam based on finite strain have been studied. Using Green-Lagrange strain tensor and comprising all of the nonlinear terms of the tensor and also applying Hamilton's principle, equations of motion and boundary conditions of the beam are obtained. Using separation method in single-harmonic state, time and locative variables are separated from each other and finally, the equations of motion and boundary conditions are gained according to locative variable. To solve the equations, generalized differential quadrature method (GDQM) is applied and then, deflection and cross-section rotation of the beam in linear and nonlinear states are drawn and compared with each other. Also, frequencies of carbon/epoxy and glass/epoxy composite beams for different boundary conditions on the basis of the finite strain are calculated. The calculated frequencies of the nonlinear free vibration of the beam utilizing finite strain assumption for various geometries have been compared to von Karman one.

• 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.

• Steel and Composite Structures
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• 제25권2호
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• pp.197-207
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• 2017

In this paper, Coriolis effect on vibration behavior of a rotating rectangular plate made of functionally graded (FG) materials under thermal loading has been investigated. The material properties of the FG plate are supposed to get changed in parallel with the thickness of the plate and the thermal properties of the material are assumed to be thermo-elastic. In this research, the effect of hub size, rotating speed and setting angle are considered. Governing equation of motion and the associated boundary conditions are obtained by Hamilton's principle. Generalized differential quadrature method (GDQM) is used to solve the governing differential equation with respect to cantilever boundary condition. The results were successfully verified with the published literatures. These results can be useful for designing rotary systems such as turbine blades. In this work, Coriolis and thermal effects are considered for the first time and GDQM method has been used in solving the equations of motion of a rotating FGM plate.

• Advances in nano research
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• 제13권3호
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• pp.233-245
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• 2022

Resently, the use of smart structures has been heightened up rapidly. For this issue, vibration analysis related to a graphene nanoplatelet composite (GPLRC) nanodisk which is attached to a piezoelectric layer and is subjected to thermal loads is explored in the current paper. The formulation of this study is obtained through the energy method and nonlocal strain gradient theory, and then it is solved employing generalized differential quadrature method (GDQM). Halpin-Tsai model in addition to the mixture's rule are utilized to capture the material properties related to the reinforced composite layer. The compatibility conditions are presented for exhibiting the perfect bounding between two layers. The results of this study are validated by employing the other published articles. The impact of such parameters as external voltage, the radius ratio, temperature difference, and nonlocality on the vibrational frequency of the system is investigated in detail.

• Earthquakes and Structures
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• 제24권2호
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• pp.111-126
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• 2023

Highly reliable and versatile methods artificial intelligence (AI) have found multiple application in the different fields of science, engineering and health care system. In the present study, we aim to utilize AI method to investigated vibrations in the human leg bone. In this regard, the bone geometry is simplified as a thick cylindrical shell structure. The deep neural network (DNN) is selected for prediction of natural frequency and critical buckling load of the bone cylindrical model. Training of the network is conducted with results of the numerical solution of the governing equations of the bone structure. A suitable optimization algorithm is selected for minimizing the loss function of the DNN. Generalized differential quadrature method (GDQM), and Hamilton's principle are used for solving and obtaining the governing equations of the system. As well as this, in the results section, with the aid of AI some predictions for improving the behaviors of the various sport systems will be given in detail.

• 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.

• Steel and Composite Structures
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• 제24권6호
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• pp.711-726
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• 2017

In the present work, by considering the agglomeration effect of single-walled carbon nanotubes, free vibration characteristics of functionally graded (FG) nanocomposite sandwich plates resting on Pasternak foundation are presented. The volume fractions of randomly oriented agglomerated single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. To determine the effect of CNT agglomeration on the elastic properties of CNT-reinforced composites, a two-parameter micromechanical model of agglomeration is employed. In this research work, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented straight CNTs. The 2-D generalized differential quadrature method (GDQM) as an efficient and accurate numerical tool is used to discretize the equations of motion and to implement the various boundary conditions. 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 benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the laminated FG nanocomposite plates are investigated. It is shown that the natural frequencies of structure are seriously affected by the influence of CNTs agglomeration. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated plates.

• 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.