• Structural Engineering and Mechanics
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• v.42 no.2
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• pp.269-289
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• 2012

Free vibration and dynamic responses of piles semi-rigidly connected with the superstructures are investigated. Timoshenko beam theory is employed to characterize the pile partially embedded in a two-parameter elastic foundation. The formulations for the method of reverberation-ray matrix (MRRM) are then derived to investigate the dynamics of the pile with surface cracks, which are modeled as massless rotational springs. Comparison with existent numerical and experimental results indicates the proposed method is very effective and accurate for dynamic analysis, especially in the high frequency range. Finally, the effects of some physical parameters on the natural frequencies, frequency responses and transient responses of the piles are studied.

• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.665-676
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• 2018

In this study, a four-node quadrilateral partial mixed plate element with low degrees of freedom (dofs) is developed for static and free vibration analysis of functionally graded material (FGM) plates rested on Winkler-Pasternak elastic foundations. The formulation of the presented finite element model is based on a parametrized mixed variational principle which is developed recently by the first author. The presented finite element model considers the effects of shear deformations and normal flexibility of the FGM plates without using any shear correction factor. It also fulfills the boundary conditions of the transverse shear and normal stresses on the top and bottom surfaces of the plate. Beside these capabilities, the number of unknown field variables of the plate is only six. The presented partial mixed finite element model has been validated through comparison with the results of the three-dimensional (3D) theory of elasticity and the results obtained from the classical and high-order plate theories available in the open literature.

• Steel and Composite Structures
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• v.26 no.4
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• pp.421-437
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• 2018

Free vibration analysis of a three-layered microbeam including an elastic micro-core and two piezo-magnetic face-sheets resting on Pasternak's foundation are studied in this paper. Strain gradient theory is used for size-dependent modeling of microbeam. In addition, three-unknown shear and normal deformations theory is employed for description of displacement field. Hamilton's principle is used for derivation of the governing equations of motion in electro-magneto-mechanical loads. Three micro-length-scale parameters based on strain gradient theory are employed for prediction of vibrational characteristics of structure in micro-scale. The results show that increase of three micro-length-scale parameters leads to significant increase of three natural frequencies especially for increase of second micro-length-scale parameter. This result is according to this fact that stiffness of a micro-scale structure is increased with increase of micro-length-scale parameters.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.9
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• pp.3110-3125
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• 2014

Network coding improves TCP's performance in lossy wireless networks. However, the complex congestion window evolution of network coded TCP (TCP-NC) makes the analysis of end-to-end throughput challenging. This paper analyzes the evolutionary process of TCP-NC against lossy links. An analytic model is established by applying a two-dimensional Markov chain. With maximum window size, end-to-end erasure rate and redundancy parameter as input parameters, the analytic model can reflect window evolution and calculate end-to-end throughput of TCP-NC precisely. The key point of our model is that by the novel definition of the states of Markov chain, both the number of related states and the computation complexity are substantially reduced. Our work helps to understand the factors that affect TCP-NC's performance and lay the foundation of its optimization. Extensive simulations on NS2 show that the analytic model features fairly high accuracy.

• Advances in nano research
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• v.5 no.4
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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.

• Coupled systems mechanics
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• v.8 no.3
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• pp.247-257
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• 2019

Fee vibrational characteristics of porous steel double-coupled nanoplate system in thermo-elastic medium is studied via a refined plate model. Different pore dispersions called uniform, symmetric and asymmetric have been defined. Nonlocal strain gradient theory (NSGT) containing two scale parameters has been adopted to stablish size-dependent modeling of the system. Hamilton's principle has been adopted to stablish 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, porosity distributions and porosity coefficient on vibration frequencies of metal foam nanoscale plates have been examined.

• Steel and Composite Structures
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• v.38 no.3
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• pp.293-304
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• 2021

The aim of this paper is to analyze the nonlinear bending of functionally graded (FG) curved nanobeams reinforced by carbon nanotubes (CNTs) in thermal environment. Chen-Yao's surface elastic theory and geometric nonlinearity are also considered. The nanobeams are subjected to uniform loadings and placed on three-parameter substrates. The Euler-Lagrange equations are employed to deduce the equations of equilibrium. Then, the asymptotic solutions and boundary value problems are analytically determined by utilizing the two-step perturbation technique. Finally, the effects of the surface parameters, geometric factors, foundation stiffness, volume fraction, thermal effects and layout type of CNTs on the nonlinear bending of the nanobeams are discussed.

• Advances in nano research
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• v.13 no.6
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• pp.599-617
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• 2022

In the present research, for the first time, the vibrational as well as buckling characteristics of a three-layered curved nanobeam including a core made of functionally graded (FG) material and two layers of smart material-piezo-magneto-electric-resting on a Winkler Pasternak elastic foundation are examined. The displacement field for the nanobeam is chosen via Timoshenko beam theory. Also, the size dependency is taken into account by using nonlocal strain gradient theory, aka NSGT. Then, by employing Hamilton's principle, energy procedure, the governing equations together with the boundary conditions are achieved. The solution procedure is a numerical solution called generalized differential quadrature method, or GDQM. The accuracy and reliability of the formulation alongside solution method is examined by using other published articles. Lastly, the parameter which can alter and affect the buckling or vocational behavior of the curved nanobeam is investigated in details.

• Steel and Composite Structures
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• v.48 no.6
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• pp.709-725
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• 2023

This paper uses a new type of deformation theory to establish the free vibration and static buckling equations of nanoplates resting on two-parameter elastic foundations, in which the flexoelectric effect is taken into account. The proposed approach used in this work is not only simpler than other higher-order shear deformation theories but also does not need any shear correction coefficients to describe exactly the mechanical responses of structures. The reliability of the theory is verified by comparing the numerical results of this work with those of analytical solutions. The results show that the flexoelectric effect significantly changes the natural frequency and the critical buckling load of the nanoplate compared with the case of neglecting this effect, especially when the plate thickness changes and with some different boundary conditions. These are new results that have not been mentioned in any publications but are meaningful in engineering practice.

• Steel and Composite Structures
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• v.35 no.1
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• pp.111-127
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• 2020

The goal of this study is to fill this apparent gap in the area about investigating the effect of porosity distributions on vibrational behavior of FG sectorial plates resting on a two-parameter elastic foundation. The response of the elastic medium is formulated by the Winkler/Pasternak model. The internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The model is proposed with material parameters varying in the thickness of plate to achieve graded distributions in both porosity and nanofillers. The elastic modulus of the nanocomposite is obtained by using Halpin-Tsai micromechanics model. The annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. The 2-D differential quadrature method as an efficient and accurate numerical approach 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. 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. Results show that for better understanding of mechanical behavior of nanocomposite plates, it is crucial to consider porosities inside the material structure.