• Structural Engineering and Mechanics
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• 제59권1호
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• pp.153-186
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• 2016

This paper addresses temperature-dependent nonlinear vibration and instability of embedded functionally graded (FG) pipes conveying viscous fluid-nanoparticle mixture. The surrounding elastic medium is modeled by temperature-dependent orthotropic Pasternak medium. Reddy third-order shear deformation theory (RSDT) of cylindrical shells are developed using the strain-displacement relations of Donnell theory. The well known Navier-Stokes equation is used for obtaining the applied force of fluid to pipe. Based on energy method and Hamilton's principal, the governing equations are derived. Generalized differential quadrature method (GDQM) is applied for obtaining the frequency and critical fluid velocity of system. The effects of different parameters such as mode numbers, nonlinearity, fluid velocity, volume percent of nanoparticle in fluid, gradient index, elastic medium, boundary condition and temperature gradient are discussed. Numerical results indicate that with increasing the stiffness of elastic medium and decreasing volume percent of nanoparticle in fluid, the frequency and critical fluid velocity increase. The presented results indicate that the material in-homogeneity has a significant influence on the vibration and instability behaviors of the FG pipes and should therefore be considered in its optimum design. In addition, fluid velocity leads to divergence and flutter instabilities.

• Structural Engineering and Mechanics
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• 제57권1호
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• pp.127-140
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• 2016

In this paper, a new first shear deformation plate theory based on neutral surface position is developed for the static and the free vibration analysis of functionally graded plates (FGPs). Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher order shear deformation theories. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Based on the present shear deformation plate theory and the neutral surface concept, the governing equations are derived from the principle of Hamilton. There is no stretching-bending coupling effect in the neutral surface based formulation. Numerical illustrations concern flexural and dynamic behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, length to thickness ratios. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Structural Engineering and Mechanics
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• 제57권1호
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• pp.105-126
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• 2016

In the present study, modelling and vibration control of axially moving laminated Carbon nanotubes/fiber/polymer composite (CNTFPC) plate under initial tension are investigated. Orthotropic visco-Pasternak foundation is developed to consider the influences of orthotropy angle, damping coefficient, normal and shear modulus. The governing equations of the laminated CNTFPC plates are derived based on new form of first-order shear deformation plate theory (FSDT) which is simpler than the conventional one due to reducing the number of unknowns and governing equations, and significantly, it does not require a shear correction factor. Halpin-Tsai model is utilized to evaluate the material properties of two-phase composite consist of uniformly distributed and randomly oriented CNTs through the epoxy resin matrix. Afterwards, the structural properties of CNT reinforced polymer matrix which is assumed as a new matrix and then reinforced with E-Glass fiber are calculated by fiber micromechanics approach. Employing Hamilton's principle, the equations of motion are obtained and solved by Hybrid analytical numerical method. Results indicate that the critical speed of moving laminated CNTFPC plate can be improved by adding appropriate values of CNTs. These findings can be used in design and manufacturing of marine vessels and aircrafts.

• Structural Engineering and Mechanics
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• 제68권6호
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• pp.721-733
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• 2018

The modal frequency responses of functionally graded (FG) sandwich doubly curved shell panels are investigated using a higher-order finite element formulation. The system of equations of the panel structure derived using Hamilton's principle for the evaluation of natural frequencies. The present shell panel model is discretised using the isoparametric Lagrangian element (nine nodes and nine degrees of freedom per node). An in-house MATLAB code is prepared using higher-order kinematics in association with the finite element scheme for the calculation of modal values. The stability of the opted numerical vibration frequency solutions for the various shell geometries i.e., single and doubly curved FG sandwich structure are proven via the convergence test. Further, close conformance of the finite element frequency solutions for the FG sandwich structures is found when compared with the published theoretical predictions (numerical, analytical and 3D elasticity solutions). Subsequently, appropriate numerical examples are solved pertaining to various design factors (curvature ratio, core-face thickness ratio, aspect ratio, support conditions, power-law index and sandwich symmetry type) those have the significant influence on the free vibration modal data of the FG sandwich curved structure.

• Structural Engineering and Mechanics
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• 제71권6호
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• pp.669-682
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• 2019

We in this article study nonlinear thermal buckling of bi-directional functionally graded beams in the theoretical frameworks of nonlocal strain graded theory. To begin with, it is assumed that the effective material properties of beams vary continuously in both the thickness and width directions. Then, we utilize a higher-order shear deformation theory that includes a physical neutral surface to derive the size-dependent governing equations combining with the Hamilton's principle and the von $K{\acute{a}}rm{\acute{a}}n$ geometric nonlinearity. It should be pointed out that the established model, containing a nonlocal parameter and a strain gradient length scale parameter, can availably account for both the influence of nonlocal elastic stress field and the influence of strain gradient stress field. Subsequently, via using a easier group of initial asymptotic solutions, the corresponding analytical solution of thermal buckling of beams is obtained with the help of perturbation method. Finally, a parametric study is carried out in detail after validating the present analysis, especially for the effects of a nonlocal parameter, a strain gradient length scale parameter and the ratio of the two on the critical thermal buckling temperature of beams.

• Structural Engineering and Mechanics
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• 제69권4호
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• pp.457-466
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• 2019

This paper presents an efficient higher-order nonlocal beam theory for the Critical buckling, of functionally graded (FG) nanobeams with porosities that may possibly occur inside the functionally graded materials (FG) during their fabrication, the nonlocal elastic behavior is described by the differential constitutive model of Eringen. The material properties of (FG) nanobeams with porosities are assumed to vary through the thickness according to a power law. The governing equations of the functionally graded nanobeams with porosities are derived by employing Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam with porosities. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, Illustrative examples are given also to show the effects of porosity volume fraction, and thickness to length ratios on the critical buckling of the FG beams.

• Structural Engineering and Mechanics
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• 제68권5호
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• pp.527-536
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• 2018

The free vibration frequency responses of the graded flat and curved (cylindrical, spherical, hyperbolic and elliptical) panel structures investigated in this research considering the rectangular and tilted planforms under unlike temperature loading. For the numerical implementation purpose, a micromechanical model is prepared with the help of Voigt's methodology via the power-law type of material model. Additionally, to incur the exact material strength, the temperature-dependent properties of each constituent of the graded structure included due to unlike thermal environment. The deformation kinematics of the rectangular/tilted graded shallow curved panel structural is modeled via higher-order type of polynomial functions. The final form of the eigenvalue equation of the heated structure obtained via Hamilton's principle and simultaneously solved numerically using finite element steps. To show the solution accuracy, a series of comparison the results are compared with the published data. Some new results are exemplified to exhibit the significance of power-law index, shallowness ratio, aspect ratio and thickness ratio on the combined thermal eigen characteristics of the regular and tilted graded panel structure.

• Structural Engineering and Mechanics
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• 제72권3호
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• pp.329-338
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• 2019

In this paper, the magnetic field influence on the wave propagation characteristics of graphene nanosheets is examined within the frame work of a two-variable plate theory. The small-scale effect is taken into consideration based on the nonlocal strain gradient theory. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. A derivation of the differential equation is conducted, employing extended principle of Hamilton and solved my means of analytical solution. A refined trigonometric two-variable plate theory is employed in Kinematic relations. The scattering relation of wave propagation in solid bodies which captures the relation of wave number and the resultant frequency is also investigated. According to the numerical results, it is revealed that the proposed modeling can provide accurate wave dispersion results of the graphene nanosheets as compared to some cases in the literature. It is shown that the wave dispersion characteristics of graphene sheets are influenced by magnetic field, elastic foundation and nonlocal parameters. Numerical results are presented to serve as benchmarks for future analyses of graphene nanosheets.

• Advances in nano research
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• 제7권3호
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• pp.157-167
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• 2019

In this paper, a classical plate model is utilized to formulate the wave propagation problem of magnetostrictive sandwich nanoplates (MSNPs) while subjected to hygrothermal loading with respect to the scale effects. Herein, magnetostriction effect is considered and controlled on the basis of a feedback control system. The nanoplate is supposed to be embedded on a visco-Pasternak substrate. The kinematic relations are derived based on the Kirchhoff plate theory; also, combining these obtained equations with Hamilton's principle, the local equations of motion are achieved. According to a nonlocal strain gradient theory (NSGT), the small scale influences are covered precisely by introducing two scale coefficients. Afterwards, the nonlocal governing equations can be derived coupling the local equations with those of the NSGT. Applying an analytical solution, the wave frequency and phase velocity of propagated waves can be gathered solving an eigenvalue problem. On the other hand, accuracy and efficiency of presented model is verified by setting a comparison between the obtained results with those of previous published researches. Effects of different variants are plotted in some figures and the highlights are discussed in detail.

• Structural Engineering and Mechanics
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• 제70권5호
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• pp.601-621
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• 2019

This study presents a comprehensive nonlinear dynamic approach to investigate the linear and nonlinear vibration of sandwich plates fabricated from functionally graded materials (FGMs) resting on an elastic foundation. Higher-order shear deformation theory and Hamilton's principle are employed to obtain governing equations. The Runge-Kutta method is employed together with the commercially available mathematical software MAPLE 14 to solve the set of nonlinear dynamic governing equations. Method validity is evaluated by comparing the results of this study and those of previous research. Good agreement is achieved. The effects of temperature change on frequencies are investigated considering various temperatures and various volume fraction index values, N. As the temperature increased, the plate frequency decreased, whereas with increasing N, the plate frequency increased. The effects of the side-to-thickness ratio, c/h, on natural frequencies were investigated. With increasing c/h, the frequencies increased nonlinearly. The effects of foundation stiffness on nonlinear vibration of the sandwich plate were also studied. Backbone curves presenting the variation of maximum displacement with respect to plate frequency are presented to provide insight into the nonlinear vibration and dynamic behavior of FGM sandwich plates.