• Coupled systems mechanics
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• 제7권4호
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• pp.373-393
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• 2018

This paper is concerned with the wave propagation behavior of rotating functionally graded temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field. Uniform, linear and nonlinear temperature distributions across the thickness are investigated. Thermo-elastic properties of FG beam change gradually according to the Mori-Tanaka distribution model in the spatial coordinate. The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function. The governing equations are derived by Hamilton's principle as a function of axial force due to centrifugal stiffening and displacement. By applying an analytical solution and solving an eigenvalue problem, the dispersion relations of rotating FG nanobeam are obtained. Numerical results illustrate that various parameters including temperature change, angular velocity, nonlocality parameter, wave number and gradient index have significant effect on the wave dispersion characteristics of the understudy nanobeam. The outcome of this study can provide beneficial information for the next generation researches and exact design of nano-machines including nanoscale molecular bearings and nanogears, etc.

• Structural Engineering and Mechanics
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• 제61권5호
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• pp.563-576
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• 2017

This paper is a continuation of the investigations started in the paper by Akbarov, S.D., Guliyev, H.H and Yahnioglu, N. (2016) "Natural vibration of the three-layered solid sphere with middle layer made of FGM: three-dimensional approach", Structural Engineering and Mechanics, 57(2), 239-263, to the case where the three-layered sphere is a hollow one. Three-dimensional exact field equations of elastodynamics are employed for investigation and the discrete-analytical method is employed for solution of the corresponding eigenvalue problem. The FGM is modelled as inhomogeneous for which the modulus of elasticity, Poison's ratio and density vary continuously through the inward radial direction according to power law distribution. Numerical results on the natural frequencies are presented and discussed. These results are also compared with the corresponding ones obtained in the previous paper by the authors. In particular, it is established that for certain harmonics and for roots of certain order, the values of the natural frequency obtained for the hollow sphere can be greater (or less) than those obtained for the solid sphere.

• Computers and Concrete
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• 제25권3호
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• pp.215-224
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• 2020

In the present study, according to the important of porosity in low specific weight in comparison of high stiffness of carbon nanotubes reinforced composite, buckling and free vibration analysis of sandwich composite beam in two configurations, of laminates using differential quadrature method (DQM) is studied. Also, the effects of porosity coefficient and three types of porosity distribution on critical buckling load and natural frequency are discussed. It is shown the buckling loads and natural frequencies of laminate 1 are significantly larger than the results of laminate 2. When configuration 2 (the core is made of FRC) and laminate 1 ([0/90/0/45/90]_s) are used, the first natural frequency rises noticeably. It is also demonstrated that the influence of the core height in the case of lower carbon volume fractions is negligible. Even though, when volume fraction of fiber increases, the critical buckling load enhances smoothly. It should be noticed the amount of decline has inverse relationship with the beam aspect ratio. Investigating three porosity patterns, beam with the distribution of porosity Type 2 has the maximum critical buckling load and first natural frequency. Among three elastic foundations (constant, linear and parabolic), buckling load and natural frequency in linear variation has the least amount. For all kind of elastic foundations, when the porosity coefficient increases, critical buckling load and natural frequency decline significantly.

• Advances in nano research
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• 제9권4호
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• pp.237-250
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• 2020

An accurate plate theory for assessing sandwich structures is of interest in order to provide precise results. Hence, this paper develops Layer-Wise (LW) theory for reaching precise results in terms of buckling and vibration behavior of Functionally Graded Carbon Nanotube-Reinforced Composite (FG-CNTRC) annular nanoplates. Furthermore, for simulating the structure much more realistic, its edges are elastically restrained against in-plane and transverse displacement. The nano structure is integrated with piezoelectric layers. Four distributions of Single-Walled Carbon Nanotubes (SWCNTs) along the thickness direction of the core layer are investigated. The Differential Quadrature Method (DQM) is utilized to solve the motion equations of nano structure subjected to the electric field. The influence of various parameters is depicted on both critical buckling load and frequency of the structure. The accuracy of solution procedure is demonstrated by comparing results with classical edge conditions. The results ascertain that the effects of different distributions of CNTs and their volume fraction are significant on the behavior of the system. Furthermore, the amount of in-plane and transverse spring coefficients plays an important role in the buckling and vibration behavior of the nano-structure and optimization of nano-structure design.

• Steel and Composite Structures
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• 제26권3호
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• pp.273-287
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• 2018

Buckling and free vibration analysis of sandwich micro plate (SMP) integrated with piezoelectric layers embedded in orthotropic Pasternak are investigated in this paper. The refined Zigzag theory (RZT) is taken into consideration to model the SMP. Four different types of functionally graded (FG) distribution through the thickness of the SMP core layer which is reinforced with single-wall carbon nanotubes (SWCNTs) are considered. The modified couple stress theory (MCST) is employed to capture the effects of small scale effects. The sandwich structure is exposed to a two dimensional magnetic field and also, piezoelectric layers are subjected to external applied voltages. In order to obtain governing equation, energy method as well as Hamilton's principle is applied. Based on an analytical solution the critical buckling loads and natural frequency are obtained. The effects of volume fraction of carbon nanotubes (CNTs), different distributions of CNTs, foundation stiffness parameters, magnetic and electric fields, small scale parameter and the thickness of piezoelectric layers on the both critical buckling loads and natural frequency of the SMP are examined. The obtained results demonstrate that the effects of volume fraction of CNTs play an important role in analyzing buckling and free vibration behavior of the SMP. Furthermore, the effects of magnetic and electric fields are remarkable on the mechanical responses of the system and cannot be neglected.

• Structural Engineering and Mechanics
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• 제67권3호
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• pp.277-281
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• 2018

The analytical solution of two functionally graded layers with Volterra type screw dislocation is investigated under anti-plane shear impact loading. The energy dissipation of FGM layers is modeled by viscous damping and the properties of the materials are assumed to change exponentially along the thickness of the layers. In this study, the rate of gradual change ofshear moduli, mass density and damping constant are assumed to be same. At first, the stress fields in the interface of the FGM layers are derived by using a single dislocation. Then, by determining a distributed dislocation density on the crack surface and by using the Fourier and Laplace integral transforms, the problem are reduce to a system ofsingular integral equations with simple Cauchy kernel. The dynamic stress intensity factors are determined by numerical Laplace inversion and the distributed dislocation technique. Finally, various examples are provided to investigate the effects of the geometrical parameters, material properties, viscous damping and cracks configuration on the dynamic fracture behavior of the interacting cracks.

• Structural Engineering and Mechanics
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• 제67권1호
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• pp.33-43
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• 2018

The dynamic output-feedback robust control method based on linear matrix inequality (LMI) method is presented for suppressing vibration response of a functionally graded material (FGM) beam with piezoelectric actuator/sensor layers in this paper. Based on the reduced model obtained by using direct mode truncation, the linear fractional state space representation of a piezoelectric FGM beam with material properties varying through the thickness is developed by considering both the inherent uncertainties in constitution material properties as well as material distribution and the model error due to mode truncation. The dynamic output-feedback robust H-infinity control law is implemented to suppress the vibration response of the piezoelectric FGM beam and the LMI method is utilized to convert control problem into convex optimization problem for efficient computation. In numerical studies, the flexural vibration control of a cantilever piezoelectric FGM beam is considered to investigate the accuracy and efficiency of the proposed control method. Compared with the efficient linear quadratic regulator (LQR) widely employed in literatures, the proposed robust control method requires less control voltage applied to the piezoelectric actuator in the case of same control performance for the controlled closed-loop system.

• Computers and Concrete
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• 제26권5호
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• pp.439-450
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• 2020

In this research, bending and buckling analyses of porous functionally graded (FG) plate under mechanical load are presented. The properties of the FG plate vary gradually across the thickness according to power-law and exponential functions. The material imperfection is considered to vary depending to a logarithmic function. The plate is modeled by a refined trigonometric shear deformation theory where the use of the shear correction factor is unnecessary. The governing equations of the FG plate are derived via virtual work principle and resolved via Navier solutions. The accuracy of the present model is checked by comparing the obtained results with those found in the literature. The various effects influencing the stresses, displacements and critical buckling loads of the plate are also examined and discussed in detail.

• Structural Engineering and Mechanics
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• 제76권1호
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• pp.115-127
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• 2020

This study presents an analytical approach to investigate the thermodynamic behavior of functionally graded beam resting on elastic foundations. The formulation is based on a refined deformation theory taking into consideration the stretching effect and the type of elastic foundation. The displacement field used in the present refined theory contains undetermined integral forms and involves only three unknowns to derive. The mechanical characteristics of the beam are assumed to be varied across the thickness according to a simple exponential law distribution. The beam is supposed simply supported and therefore the Navier solution is used to derive analytical solution. Verification examples demonstrate that the developed theory is very accurate in describing the response of FG beams subjected to thermodynamic loading. Numerical results are carried out to show the effects of the thermodynamic loading on the response of FG beams resting on elastic foundation.

• Steel and Composite Structures
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• 제28권3호
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• pp.331-347
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• 2018

In this paper history of stresses, strains, radial and circumferential displacements of a functionally graded thick-walled hollow cylinder due to creep phenomenon is investigated. The cylinder is subjected to an arbitrary non-axisymmetric two dimensional thermo-mechanical loading and uniform magnetic field along axial direction. Using equilibrium, strain-displacements and stress-strain relations, the governing differential equations of the problem containing creep strains are derived in terms of radial and circumferential displacements. Since the displacements are varying with time due to creep phenomenon, an analytical solution is not available for these equations. Thus, a semi-analytical procedure based on separation of variables and Fourier series together with a numerical procedure is employed. The numerical results indicate that the non-axisymmetric loading and the material grading index have significant effect on stress redistributions. Moreover, by proper selection of material for any combination of non-axisymmetric loading, one can arrive suitable response for the cylinder to achieve optimal design. With some simplifications, the results are validated with the existing literature.