• 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.

• Steel and Composite Structures
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• v.26 no.5
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• pp.607-620
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• 2018

Vibration analysis of deep curved FG nano-beam has been carried out based on modified couple stress theory. Material properties of curved Timoshenko beam are assumed to be functionally graded in radial direction. Governing equations of motion and related boundary conditions have been obtained via Hamilton's principle. In a parametric study, influence of length scale parameter, aspect ratio, gradient index, opening angle, mode number and interactive influences of these parameters on natural frequency of the beam, have been investigated. It was found that, considering geometrical deepness term leads to an increase in sensitivity of natural frequency about variation of aforementioned parameters.

• Advances in aircraft and spacecraft science
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• v.5 no.5
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• pp.515-531
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• 2018

In this manuscript, buckling response of the functionally graded material (FGM) nanoplate is investigated. Two opposite edges of nanoplate is under linear and nonlinear varying normal stresses. The small-scale effect is considered by Eringen's nonlocal theory. Governing equation are derived by nonlocal theory and Hamilton's principle. Navier's method is used to solve governing equation in simply boundary conditions. The obtained results exactly match the available results in the literature. The results of this research show the important role of nonlocal effect in buckling and stability behavior of nanoplates. In order to study the FG-index effect and different loading condition effects on buckling of rectangular nanoplate, Navier's method is applied and results are presented in various figures and tables.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.369-377
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• 2018

In this article, buckling and free vibration of functionally graded (FG) nanobeams resting on elastic foundation are investigated by developing various higher order beam theories which capture shear deformation influences through the thickness of the beam without the need for shear correction factors. The elastic foundation is modeled as linear Winkler springs as well as Pasternak shear layer. The material properties of FG nanobeam are supposed to change gradually along the thickness through the Mori-Tanaka model. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. From Hamilton's principle, the nonlocal governing equations of motion are derived and then solved applying analytical solution. To verify the validity of the developed theories, the results of the present work are compared with those available in literature. The effects of shear deformation, elastic foundation, gradient index, nonlocal parameter and slenderness ratio on the buckling and free vibration behavior of FG nanobeams are studied.

• Structural Engineering and Mechanics
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• v.67 no.2
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• pp.175-183
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• 2018

This research deals with the wave dispersion analysis of functionally graded double-layered nanobeam systems (FG-DNBSs) considering the piezoelectric effect based on nonlocal strain gradient theory. The nanobeam is modeled via Euler-Bernoulli beam theory. Material properties are considered to change gradually along the nanobeams' thickness on the basis of the rule of mixture. By implementing a Hamiltonian approach, the Euler-Lagrange equations of piezoelectric FG-DNBSs are obtained. Furthermore, applying an analytical solution, the dispersion relations of smart FG-DNBSs are derived by solving an eigenvalue problem. The effects of various parameters such as nonlocality, length scale parameter, interlayer stiffness, applied electric voltage, relative motions and gradient index on the wave dispersion characteristics of nanoscale beam have been investigated. Also, validity of reported results is proven in the framework of a diagram showing the convergence of this model's curve with that of a previous published attempt.

• Advances in aircraft and spacecraft science
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• v.7 no.2
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• pp.169-186
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• 2020

Based upon differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), mechanical-hygro-thermal vibrational analyzes of shear deformable porous functionally graded (FG) nanoplate on visco-elastic medium has been performed. The presented formulation incorporates two scale factors for examining vibrational behaviors of nano-dimension plates more accurately. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. It is supposed that the nano-size plate is exposed to hygro-thermal and variable compressive mechanical loadings. The governing equations achieved by Hamilton's principle are solved implementing DQM. Presented results indicate the prominence of moisture/temperature variation, damping factor, material gradient index, nonlocal coefficient, strain gradient coefficient and porosities on vibrational frequencies of FG nano-size plate.

• Steel and Composite Structures
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• v.33 no.3
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• pp.403-432
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• 2019

Axially functionally graded (AFG) beams are a new class of composite structures that have continuous variations in material and/or geometrical parameters along the axial direction. In this study, the exact analytical solutions for the free vibration of AFG and uniform beams with general elastic supports are obtained by using Euler-Bernoulli beam theory. The elastic supports are modeled with linear rotational and lateral translational springs. Moreover, the material and/or geometrical properties of the AFG beams are assumed to vary continuously and together along the length of the beam according to the power-law forms. Accordingly, the accuracy, efficiency and capability of the proposed formulations are demonstrated by comparing the responses of the numerical examples with the available solutions. In the following, the effects of the elastic end restraints and AFG parameters, namely, gradient index and gradient coefficient, on the values of the first three natural frequencies of the AFG and uniform beams are investigated comprehensively. The analytical solutions are presented in tabular and graphical forms and can be used as the benchmark solutions. Furthermore, the results presented herein can be utilized for design of inhomogeneous beams with various supporting conditions.

• Structural Engineering and Mechanics
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• v.78 no.1
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• pp.103-116
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• 2021

In this work, a model of a functionally graded (FG) nanotube conveying fluid embedded in an elastic medium is developed based on the nonlocal strain gradient theory (NSGT) in conjunction with Euler-Bernoulli beam theory (EBT). The main objective of this research is to investigate the nonlinear vibration and stability analysis of fluid-conveying nanotubes. The governing equations of motion are derived by means of Hamiltonian principle. The analytical expressions of nonlinear frequencies and critical flow velocities for two different types of boundary conditions including pinned-pinned (P-P) and clamped-clamped (C-C) conditions are obtained by employing Galerkin method as well as Hamiltonian Approach (HA). Comparison of the obtained results with the published works show the acceptable accuracy of the current solutions. The effects of the power-law index, the nonlocal and material length scale parameters and the elastic medium on the stability and nonlinear responses of FG nanotubes are thoroughly investigated and discussed.

• Steel and Composite Structures
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• v.41 no.6
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• pp.851-860
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• 2021

In this paper, a new approach of interface stress analysis in steel beam strengthened by porous FGM (Functionally Graded Materials) is presented to calculate the shear stress in the hybrid steel beam and loaded by a uniformly distributed load. The results show that there exists a high concentration of shear stress at the ends of the imperfect FGM, which might result in premature failure of the strengthening scheme at these locations. A parametric study has been conducted to investigate the sensitivity of interface behavior to parameters such as the rigidity of FGM plate (degree of homogeneity), the porosity index of FGM and the thickness of adhesive all were found to have a marked effect on the magnitude of maximum shear stress in the FGM member. we can conclude that the new approach is general in nature and may be applicable to all kinds of materials.

• Steel and Composite Structures
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• v.47 no.2
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• pp.297-313
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• 2023

This study aims to extend the application of the spectral element method (SEM) to wave propagation and free vibration analysis of functionally graded (FG) plates integrated with thin piezoelectric layers, plates with tapered thickness and structure on elastic foundations. Also, the dynamic response of the smart FG plate under impact and moving loads is presented. In this paper, the dynamic stiffness matrix of the smart rectangular FG plate is determined by using the exact dynamic shape functions based on Mindlin plate assumptions. The low computational time and results' independence with the number of elements are two significant features of the SEM. Also, to prove the accuracy and efficiency of the SEM, results are compared with Abaqus simulations and those reported in references. Furthermore, the effects of boundary conditions, power-law index, piezoelectric layers thickness, and type of loading on the results are studied.