• Structural Engineering and Mechanics
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• 제64권3호
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• pp.361-379
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• 2017

In this article, the vibration behavior of double-bonded sandwich microplates with homogeneous core and nanocomposite facesheets reinforced by carbon nanotube and boron nitride nanotube under multi physical fields such as 2D magnetic and electric fields is investigated. Symmetric and un-symmetric distributions of nanotubes are considered for facesheets of sandwich microplates such as uniform distribution and various functionally graded distributions. The double-bonded sandwich microplates rest on visco-Pasternak foundation. Material properties of sandwich microplates are obtained by the extended rule of mixture. The sinusoidal shear deformation theory (SSDT) is employed to describe displacement fields of sandwich microplates. Also, the dimensionless natural frequency is obtained by classical plate theory (CPT) and compared with the obtained results by SSDT. It can be seen that the obtained dimensionless natural frequencies by CPT are higher than SSDT. In order to study the material length scale parameters, modified strain gradient theory at micro scale is utilized and then, the equations of motion are derived using Hamilton's principle. The effects of different parameters such as foundation parameters including Winkler, shear layer and damping coefficients, various distributions and volume fraction of nanotubes, core to facesheet thickness ratio, aspect and side ratios on the dimensionless natural frequencies are discussed in details. The results of present work can be used to optimum design and control of similar systems such as micro-electro-mechanical and nano-electro-mechanical devices.

• Computers and Concrete
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• 제26권1호
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• pp.75-94
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• 2020

The aim of this research is to investigate free vibration of a novel five layer Timoshenko microbeam which consists of a transversely flexible porous core made of Al-foam, two graphen platelets (GPL) nanocomposite reinforced layers to enhance the mechanical behavior of the structure as well as two piezo-magneto-electric face sheets layers. This microbeam is subjected to a thermal load and resting on Pasternak's foundation. To accomplish the analysis, constitutive equations of each layer are derived by means of nonlocal strain gradient theory (NSGT) to capture size dependent effects. Then, the Hamilton's principle is employed to obtain the equations of motion for five layer Timoshenko microbeam. They are subsequently solved analytically by applying Navier's method so that discretized governing equations are determined in form of dynamic matrix giving the possibility to gain the natural frequencies of the Timoshenko microbeam. Eventually, after a validation study, the numerical results are presented to study and discuss the influences of various parameters such as nonlocal parameter, strain gradient parameter, aspect ratio, porosity, various volume fraction and distributions of graphene platelets, temperature change and elastic foundation coefficients on natural frequencies of the sandwich microbeam.

• Steel and Composite Structures
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• 제26권4호
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• pp.513-531
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• 2018

In this article, static, buckling and free vibration analyses of a sinusoidal micro composite beam reinforced by single-walled carbon nanotubes (SWCNTs) with considering temperature-dependent material properties embedded in an elastic medium in the presence of magnetic field under transverse uniform load are presented. This system is used at micro or sub micro scales to enhance the stiffness of micro composite structures such as bar, beam, plate and shell. In the present work, the size dependent effects based on surface stress effect and modified strain gradient theory (MSGT) are considered. The generalized rule of mixture is employed to predict temperature-dependent mechanical and thermal properties of micro composite beam. Then, the governing equations of motions are derived using Hamilton's principle and energy method. Numerical results are presented to investigate the influences of material length scale parameters, elastic foundation, composite fiber angle, magnetic intensity, temperature changes and carbon nanotubes volume fraction on the bending, buckling and free vibration behaviors of micro composite beam. There is a good agreement between the obtained results by this research and the literature results. The obtained results of this study demonstrate that the magnetic intensity, temperature changes, and two parameters elastic foundations have important effects on micro composite stiffness, while the magnetic field has greater effects on the bending, buckling and free vibration responses of micro composite beams. Moreover, it is shown that the effects of surface layers are important, and observed that the changes of carbon nanotubes volume fraction, beam length-to-thickness ratio and material length scale parameter have noticeable effects on the maximum deflection, critical buckling load and natural frequencies of micro composite beams.

• Structural Engineering and Mechanics
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• 제65권4호
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• pp.491-504
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• 2018

Because of sandwich structures with low weight and high stiffness have much usage in various industries such as civil and aerospace engineering, in this article, buckling and free vibration analyses of coupled micro composite sandwich plates are investigated based on sinusoidal shear deformation (SSDT) and most general strain gradient theories (MGSGT). It is assumed that the sandwich structure rested on an orthotropic elastic foundation and make of four composite face sheets with temperature-dependent material properties that they reinforced by carbon and boron nitride nanotubes and two flexible transversely orthotropic cores. Mathematical formulation is presented using Hamilton's principle and governing equations of motions are derived based on energy approach and applying variation method for simply supported edges under electro-magneto-thermo-mechanical, axial buckling and pre-stresses loadings. In order to predict the effects of various parameters such as material length scale parameter, length to width ratio, length to thickness ratio, thickness of face sheets to core thickness ratio, nanotubes volume fraction, pre-stress load and orthotropic elastic medium on the natural frequencies and critical buckling load of double-bonded micro composite sandwich plates. It is found that orthotropic elastic medium has a special role on the system stability and increasing Winkler and Pasternak constants lead to enhance the natural frequency and critical buckling load of micro plates, while decrease natural frequency and critical buckling load with increasing temperature changes. Also, it is showed that pre-stresses due to help the axial buckling load causes that delay the buckling phenomenon. Moreover, it is concluded that the sandwich structures with orthotropic cores have high stiffness, but because they are not economical, thus it is necessary the sandwich plates reinforce by carbon or boron nitride nanotubes specially, because these nanotubes have important thermal and mechanical properties in comparison of the other reinforcement.

• Structural Engineering and Mechanics
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• 제69권4호
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• pp.439-455
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• 2019

This research deals with thermo-electro-mechanical buckling analysis of the sandwich nano-beams with face-sheets made of functionally graded carbon nano-tubes reinforcement composite (FG-CNTRC) based on the nonlocal strain gradient elasticity theory (NSGET) considering various higher-order shear deformation beam theories (HSDBT). The sandwich nano-beam with FG-CNTRC face-sheets is subjected to thermal and electrical loads while is resting on Pasternak's foundation. It is assumed that the material properties of the face-sheets change continuously along the thickness direction according to different patterns for CNTs distribution. In order to include coupling of strain and electrical field in equation of motion, the nonlocal non-classical nano-beam model contains piezoelectric effect. The governing equations of motion are derived using Hamilton principle based on HSDBTs and NSGET. The differential quadrature method (DQM) is used to calculate the mechanical buckling loads of sandwich nano-beam as well as critical voltage and temperature rising. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various HSDBTs, length scale parameter (strain gradient parameter), the nonlocal parameter, the CNTs volume fraction, Pasternak's foundation coefficients, various boundary conditions, the CNTs efficiency parameter and geometric dimensions on the buckling behaviors of FG sandwich nano-beam. The numerical results indicate that, the amounts of the mechanical critical load calculated by PSDBT and TSDBT approximately have same values as well as ESDBT and ASDBT. Also, it is worthy noted that buckling load calculated by aforementioned theories is nearly smaller than buckling load estimated by FSDBT. Also, similar aforementioned structure is used to building the nano/micro oscillators.

• Smart Structures and Systems
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• 제25권5호
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• pp.581-592
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• 2020

Magneto-rheological fluids and magneto-strictive materials are of the well-known smart materials which are used to control and reduce the vibrations of the structures. Vibration analysis of a smart annular three-layered plate is provided in this work. MR fluids are used as the core's material type and the face sheets are made from MS materials and is assumed they are fully bonded to each other. The structure is rested on visco-Pasternak foundation and also is subjected to a transverse magnetic field. The governing motion equations are derived based on CPT and employing Hamilton's principle and are solved via GDQ as a numerical method for various boundary conditions. Effect of different parameters on the results are considered and discussed in detail. One of the salient features of this work is the consideration of MR fluids as the core, MS materials as the faces, and all of them under magnetic field. The outcomes of this study may be led to design and create smart structures such as sensors, actuators and also dampers.

• Smart Structures and Systems
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• 제18권5호
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• pp.1029-1062
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• 2016

In this research, the nonlinear free vibration analysis of boron-nitride micro ribbon (BNMR) on the Pasternak elastic foundation under electrical, mechanical and thermal loadings using modified strain gradient theory (MSGT) is studied. Employing the von $K{\acute{a}}rm{\acute{a}}n$ nonlinear geometry theory, the nonlinear equations of motion for the graphene micro ribbon (GMR) using Euler-Bernoulli beam model with considering attached mass and size effects based on Hamilton's principle is obtained. These equations are converted into the nonlinear ordinary differential equations by elimination of the time variable using Kantorovich time-averaging method. To determine nonlinear frequency of GMR under various boundary conditions, and considering mass effect, differential quadrature element method (DQEM) is used. Based on modified strain MSGT, the results of the current model are compared with the obtained results by classical and modified couple stress theories (CT and MCST). Furthermore, the effect of various parameters such as material length scale parameter, attached mass, temperature change, piezoelectric coefficient, two parameters of elastic foundations on the natural frequencies of BNMR is investigated. The results show that for all boundary conditions, by increasing the mass intensity in a fixed position, the linear and nonlinear natural frequency of the GMR reduces. In addition, with increasing of material length scale parameter, the frequency ratio decreases. This results can be used to design and control nano/micro devices and nano electronics to avoid resonance phenomenon.

• Advances in nano research
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• 제5권2호
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• pp.141-169
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• 2017

In this paper, a nanobeam connected to a rotating molecular hub is considered. The vibration behavior of rotating functionally graded nanobeam based on Eringen's nonlocal theory and Euler-Bernoulli beam model is investigated. Furthermore, axial preload and porosity effect is studied. It is supposed that the material attributes of the functionally graded porous nanobeam, varies continuously in the thickness direction according to the power law model considering the even distribution of porosities. Porosity at the nanoscopic length scale can affect on the rotating functionally graded nanobeams dynamics. The equations of motion and the associated boundary conditions are derived through the Hamilton's principle and generalized differential quadrature method (GDQM) is utilized to solve the equations. In this paper, the influences of some parameters such as functionally graded power (FG-index), porosity parameter, axial preload, nonlocal parameter and angular velocity on natural frequencies of rotating nanobeams with pure ceramic, pure metal and functionally graded materials are examined and some comparisons about the influence of various parameters on the natural frequencies corresponding to the simply-simply, simplyclamped, clamped-clamped boundary conditions are carried out.

• Advances in nano research
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• 제8권1호
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• pp.69-82
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• 2020

In this study, the free and forced vibration analysis of micro sandwich plate with porous core layer and magneto-electric face sheets based on modified couple stress theory and first order shear deformation theory under simply supported boundary conditions is illustrated. It is noted that the core layer is composed from balsa wood and also piezo magneto-electric facesheets are made of BiTiO₃-CoFe₂O₄. Using Hamilton's principle, the equations of motion for micro sandwich plate are obtained. Also, the Navier's method for simply support boundary condition is used to solve these equations. The effects of applied voltage, magnetic field, length to width ratio, thickness of porous to micro plate thickness ratio, type of porous, coefficient of porous on the frequency ratio are investigated. The numerical results indicate that with increasing of the porous coefficient, the non-dimensional frequency increases. Also, with an increase in the electric potential, the non-dimensional frequency decreases, while and with increasing of the magnetic potential is vice versa.

• Steel and Composite Structures
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• 제33권1호
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• pp.93-109
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• 2019

In the present study, vibration analysis of double bonded micro sandwich cylindrical shells with saturated porous core and carbon/boron nitride nanotubes (CNT/BNNT) reinforced composite face sheets under multi-physical loadings based on Cooper-Naghdi theory is investigated. The material properties of the micro structure are assumed to be temperature dependent, and each of the micro-tubes is placed on the Pasternak elastic foundations, and mechanical, moisture, thermal, electrical, and magnetic forces are effective on the structural behavior. The distributions of porous materials in three distributions such as non-linear non-symmetric, nonlinear-symmetric, and uniform are considered. The relationship including electro-magneto-hydro-thermo-mechanical loadings based on modified couple stress theory is obtained and moreover the governing equations of motion using the energy method and the Hamilton's principle are derived. Also, Navier's type solution is also used to solve the governing equations of motion. The effects of various parameters such as material length scale parameter, temperature change, various distributions of nanotube, volume fraction of nanotubes, porosity and Skempton coefficients, and geometric parameters on the natural frequency of double bonded micro sandwich cylindrical shells are investigated. Increasing the porosity and the Skempton coefficients of the core in micro sandwich cylindrical shell lead to increase the natural frequency of the structure. Cylindrical shells and porous materials in the industry of filters and separators, heat exchangers and coolers are widely used and are generally accepted today.