• Structural Engineering and Mechanics
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• 제72권1호
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• pp.113-129
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• 2019

A four-variable shear deformation refined plate theory has been proposed for dynamic characteristics of smart plates made of porous magneto-electro-elastic functionally graded (MEE-FG) materials with various boundary conditions by using an analytical method. Magneto-electro-elastic properties of FGM plate are supposed to vary through the thickness direction and are estimated through the modified power-law rule in which the porosities with even and uneven type are approximated. Pores possibly occur inside functionally graded materials (FGMs) due the result of technical problems that lead to creation of micro-voids in these materials. The variation of pores along the thickness direction influences the mechanical properties. The governing differential equations and boundary conditions of embedded porous FGM plate under magneto-electrical field are derived through Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factors. An analytical solution procedure is used to achieve the natural frequencies of embedded porous FG plate supposed to magneto-electrical field with various boundary condition. A parametric study is led to carry out the effects of material graduation exponent, coefficient of porosity, magnetic potential, electric voltage, elastic foundation parameters, various boundary conditions and plate side-to-thickness ratio on natural frequencies of the porous MEE-FG plate. It is concluded that these parameters play significant roles on the dynamic behavior of porous MEE-FG plates. Presented numerical results can serve as benchmarks for future analyses of MEE-FG plates with porosity phases.

• Advances in nano research
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• 제5권4호
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• pp.281-301
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• 2017

In this disquisition, an exact solution method is developed for analyzing the vibration characteristics of magneto-electro-elastic functionally graded (MEE-FG) beams by considering porosity distribution and various boundary conditions via a four-variable shear deformation refined beam theory for the first time. Magneto-electroelastic properties of porous FG beam are supposed to vary through the thickness direction and are modeled via modified power-law rule which is formulated using the concept of even and uneven porosity distributions. Porosities possibly occurring inside functionally graded materials (FGMs) during fabrication because of technical problem that lead to creation micro-voids in FG materials. So, it is necessary to consider the effect of porosities on the vibration behavior of MEE-FG beam in the present study. The governing differential equations and related boundary conditions of porous MEE-FG beam subjected to physical field are derived by Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factor. An analytical solution procedure is used to achieve the natural frequencies of porous-FG beam supposed to magneto-electrical field which satisfies various boundary conditions. A parametric study is led to carry out the effects of material graduation exponent, porosity parameter, external magnetic potential, external electric voltage, slenderness ratio and various boundary conditions on dimensionless frequencies of porous MEE-FG beam. It is concluded that these parameters play noticeable roles on the vibration behavior of MEE-FG beam with porosities. Presented numerical results can be applied as benchmarks for future design of MEE-FG structures with porosity phases.

• Steel and Composite Structures
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• 제25권2호
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• pp.141-155
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• 2017

This paper presents an investigation into the magneto-thermo-mechanical vibration and damping of a viscoelastic functionally graded-carbon nanotubes (FG-CNTs)-reinforced curved microbeam based on Timoshenko beam and strain gradient theories. The structure is surrounded by a viscoelastic medium which is simulated with spring, damper and shear elements. The effective temperature-dependent material properties of the CNTs-reinforced composite beam are obtained using the extended rule of mixture. The structure is assumed to be subjected to a longitudinal magnetic field. The governing equations of motion are derived using Hamilton's principle and solved by employing differential quadrature method (DQM). The effect of various parameter like volume percent and distribution type of CNTs, temperature change, magnetic field, boundary conditions, material length scale parameter, central angle, viscoelastic medium and structural damping on the vibration and damping behaviors of the nanocomposite curved microbeam is examined. The results show that with increasing volume percent of CNTs and considering magnetic field, material length scale parameter and viscoelastic medium, the frequency of the system increases and critically damped situation occurs at higher values of damper constant. In addition, the structure with FGX distribution type of CNTs has the highest stiffness. It is also observed that increasing temperature, structural damping and central angle of curved microbeam decreases the frequency of the system.

• Computers and Concrete
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• 제21권6호
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• pp.717-726
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• 2018

Concrete pipelines are the most efficient and safe means for gas and oil transportation over a long distance. The use of nano materials and nono-engineering can be considered for enhancing concrete pipelines properties. the tests show that $SiO_2$ nanoparticles can improve the mechanical behavior of concrete. Moreover, severe hazard for pipelines is seismic ground motion. Over the years, scientists have attempted to understand pipe behavior against earthquake most frequently via numerical modeling and simulation. Therefore, in this paper, the dynamic response of underwater nanocomposite submerged pipeline conveying fluid is studied. The structure is subjected to the dynamic loads caused by earthquake and the governing equations of the system are derived using mathematical model via Classic shell theory and Hamilton's principle. Navier-Stokes equation is employed to calculate the force due to the fluid in the pipe. As well, the effect of external fluid is modeled with an external force. Mori-Tanaka approach is used to estimate the equivalent material properties of the nanocomposite. 1978 Tabas earthquake in Iran is considered for modelling seismic load. The dynamic displacement of the structure is extracted using differential quadrature method (DQM) and Newmark method. The effects of different parameters such as $SiO_2$ nanoparticles volume percent, boundary conditions, thickness to radius ratios, length to radius ratios, internal and external fluid pressure and earthquake intensity are discussed on the seismic response of the structure. From results obtained in this paper, it can be found that the dynamic response of the pipe is increased in the presence of internal and external fluid. Furthermore, the use of $SiO_2$ nanoparticles in concrete pipeline reduces the displacement of the structure during an earthquake.

• Computers and Concrete
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• 제24권2호
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• pp.125-135
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• 2019

Concrete pipelines are the most efficient and safe means for gas and oil transportation over a long distance. The use of nano materials and nono-engineering can be considered for enhancing concrete pipelines properties. the tests show that SiO2 nanoparticles can improve the mechanical behavior of concrete. Moreover, severe hazard for pipelines is seismic ground motion. Over the years, scientists have attempted to understand pipe behavior against earthquake most frequently via numerical modeling and simulation. Therefore, in this paper, the dynamic response of underwater nanocomposite submerged pipeline conveying fluid is studied. The structure is subjected to the dynamic loads caused by earthquake and the governing equations of the system are derived using mathematical model via Classic shell theory and Hamilton's principle. Navier-Stokes equation is employed to calculate the force due to the fluid in the pipe. As well, the effect of external fluid is modeled with an external force. Mori-Tanaka approach is used to estimate the equivalent material properties of the nanocomposite. 1978 Tabas earthquake in Iran is considered for modelling seismic load. The dynamic displacement of the structure is extracted using differential quadrature method (DQM) and Newmark method. The effects of different parameters such as SiO2 nanoparticles volume percent, boundary conditions, thickness to radius ratios, length to radius ratios, internal and external fluid pressure and earthquake intensity are discussed on the seismic response of the structure. From results obtained in this paper, it can be found that the dynamic response of the pipe is increased in the presence of internal and external fluid. Furthermore, the use of SiO2 nanoparticles in concrete pipeline reduces the displacement of the structure during an earthquake.

• Steel and Composite Structures
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• 제31권5호
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• pp.503-516
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• 2019

This work presents a dynamic investigation of functionally graded (FG) plates resting on elastic foundation using a simple quasi-3D higher shear deformation theory (quasi-3D HSDT) in which the stretching effect is considered. The culmination of this theory is that in addition to taking into account the effect of thickness extension (${\varepsilon}_z{\neq}0$), the kinematic is defined with only 4 unknowns, which is even lower than the first order shear deformation theory (FSDT). The elastic foundation is included in the formulation using the Pasternak mathematical model. The governing equations are deduced through the Hamilton's principle. These equations are then solved via closed-type solutions of the Navier type. The fundamental frequencies are predicted by solving the eigenvalue problem. The degree of accuracy of present solutions can be shown by comparing it to the 3D solution and other closed-form solutions available in the literature.

• Earthquakes and Structures
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• 제22권5호
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• pp.447-460
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• 2022

In this article, wave propagation in functional gradation plates (FG) resting on an elastic foundation with two parameters is studied using a new quasi-three-dimensional (3D) higher shear deformation theory (HSDT). The new qausi-3D HSOT has only five variables in fields displacement, which means has few numbers of unknowns compared with others quasi-3D. This higher shear deformation theory (HSDT) includes shear deformation and effect stretching with satisfying the boundary conditions of zero traction on the surfaces of the FG plate without the need for shear correction factors. The FG plates are considered to rest on the Winkler layer, which is interconnected with a Pasternak shear layer. The properties of the material graded for the plates are supposed to vary smoothly, with the power and the exponential law, in the z-direction. By based on Hamilton's principle, we derive the governing equations of FG plates resting on an elastic foundation, which are then solved analytically to obtain the dispersion relations. Numerical results are presented in the form of graphs and tables to demonstrate the effectiveness of the current quasi-3D theory and to analyze the effect of the elastic foundation on wave propagation in FG plates.

• Steel and Composite Structures
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• 제44권1호
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• pp.81-89
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• 2022

The purposes of the present work it to study the effect of shear deformation on the static post-buckling response of simply supported functionally graded (FGM) axisymmetric beams based on classical, first-order, and higher-order shear deformation theories. The behavior of postbuckling is introduced based on geometric nonlinearity. The material properties of functionally graded materials (FGM) are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The equations of motion and the boundary conditions derived using Hamilton's principle. This article compares and addresses the efficiency, the applicability, and the limits of classical models, higher order models (CLT, FSDT, and HSDT) for the static post-buckling response of an asymmetrically simply supported FGM beam. The amplitude of the static post-buckling obtained a solving the nonlinear governing equations. The results showing the variation of the maximum post-buckling amplitude with the applied axial load presented, for different theory and different parameters of material and geometry. In conclusion: The shear effect found to have a significant contribution to the post-buckling behaviors of axisymmetric beams. As well as the classical beam theory CBT, underestimate the shear effect compared to higher order shear deformation theories HSDT.

• Steel and Composite Structures
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• 제42권6호
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• pp.805-826
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• 2022

The free and live load-forced vibration behaviour of porous functionally graded (PFG) higher order nanobeams in the thermal and magnetic fields is investigated comprehensively through this work in the framework of nonlocal strain gradient theory (NLSGT). The porosity effects on the dynamic behaviour of FG nanobeams is investigated using four different porosity distribution models. These models are exploited; uniform, symmetrical, condensed upward, and condensed downward distributions. The material characteristics gradation in the thickness direction is estimated using the power-law. The magnetic field effect is incorporated using Maxwell's equations. The third order shear deformation beam theory is adopted to incorporate the shear deformation effect. The Hamilton principle is adopted to derive the coupled thermomagnetic dynamic equations of motion of the whole system and the associated boundary conditions. Navier method is used to derive the analytical solution of the governing equations. The developed methodology is verified and compared with the available results in the literature and good agreement is observed. Parametric studies are conducted to show effects of porosity parameter; porosity distribution, temperature rise, magnetic field intensity, material gradation index, non-classical parameters, and the applied moving load velocity on the vibration behavior of nanobeams. It has been showed that all the analyzed conditions have significant effects on the dynamic behavior of the nanobeams. Additionally, it has been observed that the negative effects of moving load, porosity and thermal load on the nanobeam dynamics can be reduced by the effect of the force induced from the directed magnetic field or can be kept within certain desired design limits by controlling the intensity of the magnetic field.

• Advances in nano research
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• 제12권1호
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• pp.73-79
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• 2022

Due to the extensive use of concrete structures in various applications, the improvement of their strength and quality has become of great importance. A new way of achieving this purpose is to add different types of nanoparticles to concrete admixtures. In this work, a mathematical model has been employed to analyze the vibration of concrete beams reinforced by graphene oxide (GO) nanoparticles. To verify the accuracy of the presented model, an experimental study has been conducted to compare the compressive strengths of these beams. Since GO nanoparticles are not readily dissolved in water, before producing the concrete samples, the GO nanoparticles are dispersed in the mixture by using a shaker, magnetic striker, ultrasonic devices, and finally, by means of a mechanical mixer. The sinusoidal shear deformation beam theory (SSDBT) is employed to model the concrete beams. The Mori-Tanaka model is used to determine the effective properties of the structure, including the agglomeration influences. The motion equations are calculated by applying the energy method and Hamilton's principle. The vibration frequencies of the concrete beam samples are obtained by an analytical method. Three samples containing 0.02% GO nanoparticles are made and their compressive strengths are measured and compared. There is a good agreement between our results and those of the mathematical model and other papers, with a maximum difference of 1.29% between them. The aim of this work is to investigate the effects of nanoparticle volume fraction and agglomeration and the influences of beam length and thickness on the vibration frequency of concrete structures. The results show that by adding the GO nanoparticles, the vibration frequency of the beams is increased.