• Steel and Composite Structures
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• v.26 no.3
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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.

• Steel and Composite Structures
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• v.50 no.1
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• pp.63-75
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• 2024

In this paper, the modified couple stress theory (MCST) and first order shear deformation theory (FSDT) are employed to investigate the free vibration and bending analyses of a three-layered micro-shell sandwiched by piezoelectric layers subjected to an applied voltage and reinforced graphene nanoplatelets (GPLs) under external and internal pressure. The micro-shell is resting on an elastic foundation modeled as Pasternak model. The mixture's rule and Halpin-Tsai model are utilized to compute the effective mechanical properties. By applying Hamilton's principle, the motion equations and associated boundary conditions are derived. Static/ dynamic results are obtained using Navier's method. The results are validated with the previously published works. The numerical results are presented to study and discuss the influences of various parameters on the natural frequencies and deflection of the micro-shell, such as applied voltage, thickness of the piezoelectric layer to radius, length to radius ratio, volume fraction and various distribution pattern of the GPLs, thickness-to-length scale parameter, and foundation coefficients for the both external and internal pressure. The main novelty of this work is simultaneous effect of graphene nanoplatelets as reinforcement and piezoelectric layers on the bending and vibration characteristics of the sandwich micro shell.

• Structural Engineering and Mechanics
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• v.90 no.3
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• pp.219-232
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• 2024

In current study, for the first time, Nonlinear Bending of a skew microplate made of a laminated composite strengthened with graphene nanosheets is investigated. A mixture of mechanical and thermal stresses is applied to the plate, and the reaction is analyzed using the First Shear Deformation Theory (FSDT). Since different percentages of graphene sheets are included in the multilayer structure of the composite, the characteristics of the composite are functionally graded throughout its thickness. Halpin-Tsai models are used to characterize mechanical qualities, whereas Schapery models are used to characterize thermal properties. The microplate's non-linear strain is first calculated by calculating the plate shear deformation and using the Green-Lagrange tensor and von Karman assumptions. Then the elements of the Couple and Cauchy stress tensors using the Modified Coupled Stress Theory (MCST) are derived. Next, using the Hamilton Principle, the microplate's governing equations and associated boundary conditions are calculated. The nonlinear differential equations are linearized by utilizing auxiliary variables in the nonlinear solution by applying the Frechet approach. The linearized equations are rectified via an iterative loop to precisely solve the problem. For this, the Differential Quadrature Method (DQM) is utilized, and the outcomes are shown for the basic support boundary condition. To ascertain the maximum values of microplate deflection for a range of circumstances-such as skew angles, volume fractions, configurations, temperatures, and length scales-a parametric analysis is carried out. To shed light on how the microplate behaves in these various circumstances, the resulting results are analyzed.

• Computers and Concrete
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• v.32 no.5
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• pp.439-454
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• 2023

In this article, the surface stress effects on the buckling analysis of the annular sandwich plate is developed. The proposed plate is composed of two face layers made of carbon nanotubes (CNT) reinforced composite with assuming of fully bonded to functionally graded porous core. The generalized rule of the mixture is employed to predict the mechanical properties of the microcomposite sandwich plate. The derived potentials energy based on higher order shear deformation theory (HSDT) and modified couple stress theory (MCST) is solved by employing the Ritz method. An exact analytical solution is presented to calculate the critical buckling loads of the annular sandwich plate. The predicted results are validated by carrying out the comparison studies for the buckling analysis of annular plates with those obtained by other analytical and finite element methods. The effects of various parameters such as material length scale parameter, core thickness to total thickness ratio (hc/h), surface elastic constants based on surface stress effect, various boundary condition and porosity distributions, size of the internal pores (e0), Skempton coefficient and elastic foundation on the critical buckling load have been studied. The results can be served as benchmark data for future works and also in the design of materials science, injunction high-pressure micropipe connections, nanotechnology, and smart systems.

• Steel and Composite Structures
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• v.32 no.6
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• pp.753-767
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• 2019

Vibration control in mechanical equipments is an important problem where unwanted vibrations are vanish or at least diminished. In this paper, free vibration active control of the porous sandwich piezoelectric polymeric nanocomposite microbeam with microsensor and microactuater layers are investigated. The aim of this research is to reduce amplitude of vibration in micro beam based on linear quadratic regulator (LQR). Modified couple stress theory (MCST) according to sinusoidal shear deformation theory is presented. The porous sandwich microbeam is rested on elastic foundation. The core and face sheet are made of porous and three-phase carbon nanotubes/resin/fiber nanocomposite materials. The equations of motion are extracted by Hamilton's principle and then Navier's type solution are employed for solving them. The governing equations of motion are written in space state form and linear quadratic regulator (LQR) is used for active control approach. The various parameters are conducted to investigate on the frequency response function (FRF) of the sandwich microbeam for vibration active control. The results indicate that the higher length scale to the thickness, the face sheet thickness to total thickness and the considering microsensor and microactutor significantly affect LQR and uncontrolled FRF. Also, the porosity coefficient increasing, Skempton coefficient and Winkler spring constant shift the frequency response to higher frequencies. The obtained results can be useful for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.

• Steel and Composite Structures
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• v.41 no.6
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• pp.805-820
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• 2021

In this research, the buckling and free vibration of three-phase carbon nanotubes/ fiber/ polymer piezoelectric nanocomposite face sheet sandwich microbeam with microsensor and micro-actuator surrounded in elastic foundation based on modified couple stress theory (MCST) is investigated. Three types of porous materials are considered for sandwich core. Higher order (Reddy) and sinusoidal shear deformation beam theories are employed for the displacement fields. Sinusoidal surface stress effects are extracted for sinusoidal shear deformation beam theory. The equations of motion are derived by Hamilton's principle and then the natural frequency and critical buckling load are obtained by Navier's type solution. The determined results are in good agreement with other literatures. The detailed numerical investigation for various parameters is performed for this microsensor-microactuator. The results reveal that the microsensor-microactuator enhanced by increasing of Skempton coefficient, carbon nanotubes diameter length to thickness ratio, small scale factor, elastic foundation, surface stress constants and reduction in porous coefficient, micro-actuator voltage and CNT weight fraction. The valuable results can be expedient for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.

• Smart Structures and Systems
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• v.18 no.5
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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.

• Structural Engineering and Mechanics
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• v.64 no.5
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• pp.527-541
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• 2017

In this work, a new hyperbolic shear deformation beam theory is proposed based on a modified couple stress theory (MCST) to investigate the bending and free vibration responses of functionally graded (FG) micro beam made of porous material. This non-classical micro-beam model introduces the material length scale coefficient which can capture the size influence. The non-classical beam model reduces to the classical beam model when the material length scale coefficient is set to zero. The mechanical material properties of the FG micro-beam are assumed to vary in the thickness direction and are estimated through the classical rule of mixture which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. Effects of several important parameters such as power-law exponents, porosity distributions, porosity volume fractions, the material length scale parameter and slenderness ratios on bending and dynamic responses of FG micro-beams are investigated and discussed in detail. It is concluded that these effects play significant role in the mechanical behavior of porous FG micro-beams.

• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.225-238
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• 2020

This work treats the axisymmetric buckling of functionally graded (FG) porous annular/circular nanoplates based on modified couple stress theory (MCST). The nanoplate is located at the elastic medium which is simulated by Kerr foundation with two spring and one shear layer. The material properties of the porous FG nanostructure are assumed to vary through the nanoplate thickness based on power-law rule. Based on two variables refined plate theory, the governing equations are derived by utilizing Hamilton's principle. Applying generalized differential quadrature method (GDQM), the buckling load of the annular/circular nanoplates is obtained for different boundary conditions. The influences of different involved parameters such as boundary conditions, Kerr medium, material length scale parameter, geometrical parameters of the nanoplate, FG power index and porosity are demonstrated on the nonlinear buckling load of the annular/circular nanoplates. The results indicate that with increasing the porosity of the nanoplate, the nonlinear buckling load is decreased. In addition, with increasing the material length scale parameter to thickness ratio, the effect of spring constant of Kerr foundation on the buckling load becomes more prominent. The present results are compared with those available in the literature to validate the accuracy and reliability. A good agreement is observed between the two sets of the results.

• Computers and Concrete
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• v.24 no.3
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• pp.185-192
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• 2019

In this paper, the buckling of micro sandwich hollow circular plate is investigated with the consideration of the porous core and piezoelectric layer reinforced by functionally graded (FG)carbon nano-tube. For modeling the displacement field of sandwich hollow circular plate, the high-order shear deformation theory (HSDT) of plate and modified couple stress theory (MCST) are used. The governing differential equations of the system can be derived using the principle of minimum potential energy and Maxwell's equation that for solving these equations, the Ritz method is employed. The results of this research indicate the influence of various parameters such as porous coefficients, small length scale parameter, distribution of carbon nano-tube in piezoelectric layers and temperature on critical buckling load. The purpose of this research is to show the effect of physical parameters on the critical buckling load of micro sandwich plate and then optimize these parameters to design structures with the best efficiency. The results of this research can be used for optimization of micro-structures and manufacturing different structure in aircraft and aerospace.