• Steel and Composite Structures
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• 제27권3호
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• pp.371-388
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• 2018

In this paper, a new model based on nonlocal high order theory is proposed to study the size effect on the bending of nano-sandwich beams with a compliance core. In this model, in contrast to most of the available sandwich theories, no prior assumptions are made with respect to the displacement field in the core. Herein the displacement and the stress fields of the core are obtained through an elasticity solution. Equations of motion and boundary conditions for nano-sandwich beam are derived by using Hamilton's principle and an analytical solution is presented for simply supported nano-sandwich beam. The results are validated with previous studies in the literature. These results can be utilized in the study of nano-sensors and nano-actuators. The effect of nonlocal parameter, Young's modulus of the core and aspect ratio on the deflection of the nano-sandwich beam is investigated. It is concluded that by including the small-scale effects, the deflection of the skins is increased and by increasing the nonlocal parameter, the influence of small-scale effects on the deflections is increased.

• Smart Structures and Systems
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• 제22권1호
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• pp.105-120
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• 2018

In this paper, the nonlinear free and forced vibration responses of sandwich nano-beams with three various functionally graded (FG) patterns of reinforced carbon nanotubes (CNTs) face-sheets are investigated. The sandwich nano-beam is resting on nonlinear Visco-elastic foundation and is subjected to thermal and electrical loads. The nonlinear governing equations of motion are derived for an Euler-Bernoulli beam based on Hamilton principle and von Karman nonlinear relation. To analyze nonlinear vibration, Galerkin's decomposition technique is employed to convert the governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE). Furthermore, the Multiple Times Scale (MTS) method is employed to find approximate solution for the nonlinear time, frequency and forced responses of the sandwich nano-beam. Comparison between results of this paper and previous published paper shows that our numerical results are in good agreement with literature. In addition, the nonlinear frequency, force response and nonlinear damping time response is carefully studied. The influences of important parameters such as nonlocal parameter, volume fraction of the CNTs, different patterns of CNTs, length scale parameter, Visco-Pasternak foundation parameter, applied voltage, longitudinal magnetic field and temperature change are investigated on the various responses. One can conclude that frequency of FG-AV pattern is greater than other used patterns.

• Smart Structures and Systems
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• 제20권3호
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• pp.329-342
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• 2017

In this paper, the dispersion characteristics of elastic waves propagation in sandwich nano-beams with functionally graded (FG) face-sheets reinforced with carbon nanotubes (CNTs) is investigated based on various high order shear deformation beam theories (HOSDBTs) as well as nonlocal strain gradient theory (NSGT). In order to align CNTs as symmetric and asymmetric in top and bottom face-sheets with respect to neutral geometric axis of the sandwich nano-beam, various patterns are employed in this analysis. The sandwich nano-beam resting on Pasternak foundation is subjected to thermal, magnetic and electrical fields. In order to involve small scale parameter in governing equations, the NSGT is employed for this analysis. The governing equations of motion are derived using Hamilton's principle based on various HSDBTs. Then the governing equations are solved using analytical method. A detailed parametric study is conducted to study the effects of length scale parameter, different HSDBTs, the nonlocal parameter, various aligning of CNTs in thickness direction of face-sheets, different volume fraction of CNTs, foundation stiffness, applied voltage, magnetic intensity field and temperature change on the wave propagation characteristics of sandwich nano-beam. Also cut-off frequency and phase velocity are investigated in detail. According to results obtained, UU and VA patterns have the same cut-off frequency value but AV pattern has the lower value with respect to them.

• Steel and Composite Structures
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• 제31권3호
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• pp.261-276
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• 2019

The study investigates the free vibration of a nano-scale sandwich beam by an extended high order approach, which has not been reported in the existing literature. First-order shear deformation theory for steel skins and so-called high-order sandwich panel theory for the core are applied. Next, the modified couple stress theory is used for both skins and cores. The Hamilton principle is utilized for deriving equations and corresponding boundary conditions. First, in the study the three-mode shapes natural frequencies for various material parameters are investigated. Also, obtained results are evaluated for two types of stiff and soft cores and isotropic, homogenous steel skins. In the research since the governing equations and also the boundary conditions are nonhomogeneous, therefore some closed-form solutions are not applicable. So, to obtain natural frequencies, the boundary conditions are converted to initial conditions called the shooting method as the numerical one. This method is one of the most robust approaches to solve complex equations and boundary conditions. Moreover, three types of simply supported on both sides of the beam (S-S), simply on one side and clamp supported on the other one (S-C) and clamped supported on both sides (C-C) are scrutinized. The parametric study is followed to evaluate the effect of nano-size scale, geometrical configurations for skins, core and material property change for cores as well. Results show that natural frequencies increase by an increase in skins thickness and core Young modulus and a decrease in beam length, core thickness as well. Furthermore, differences between obtained frequencies for soft and stiff cores increase in higher mode shapes; while, the more differences are evaluated for the stiff one.

• 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.

• Advances in nano research
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• 제17권3호
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• pp.275-284
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• 2024

In this article, a nonlocal stress-strain elasticity theory on the vibration analysis of Timoshenko sandwich beam theory with symmetric and asymmetric distributions of porous core and functionally graded material facesheets is introduced. According to nonlocal elasticity Eringen's theory (nonlocal stress elasticity theory), the stress at a reference point in the body is dependent not only on the strain state at that point, but also on the strain state at all of the points throughout the body; while, according to a new nonlocal strain elasticity theory, the strain at a reference point in the body is dependent not only on the stress state at that point, but also on the stress state at all of the points throughout the body. Also, with combinations of two concepts, the nonlocal stress-strain elasticity theory is defined that can be actual at micro/nano scales. It is concluded that the natural frequency decreases with an increase in the nonlocal stress parameter; while, this effect is vice versa for nonlocal strain elasticity, because the stiffness of Timoshenko sandwich beam decreases with increasing of the nonlocal stress parameter; in which, the nonlocal strain parameter leads to increase the stiffness of structures at micro/nano scale. It is seen that the natural frequency by considering both nonlocal stress parameter and nonlocal strain parameter is higher than the nonlocal stress parameter only and lower for a nonlocal strain parameter only.

• Advances in nano research
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• 제14권2호
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• pp.141-154
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• 2023

Effects of viscoelastic foundation on vibration of curved-beam structure with clamped and simply-supported boundary conditions is investigated in this study. In doing so, a micro-scale laminate composite beam with two piezoelectric face layer with a carbon nanotube reinforces composite core is considered. The whole beam structure is laid on a viscoelastic substrate which normally occurred in actual conditions. Due to small scale of the structure non-classical elasticity theory provided more accurate results. Therefore, nonlocal strain gradient theory is employed here to capture both nano-scale effects on carbon nanotubes and microscale effects because of overall scale of the structure. Equivalent homogenous properties of the composite core is obtained using Halpin-Tsai equation. The equations of motion is derived considering energy terms of the beam and variational principle in minimizing total energy. The boundary condition is assumed to be clamped at one end and simply supported at the other end. Due to nonlinear terms in the equations of motion, semi-analytical method of general differential quadrature method is engaged to solve the equations. In addition, due to complexity in developing and solving equations of motion of arches, an artificial neural network is design and implemented to capture effects of different parameters on the inplane vibration of sandwich arches. At the end, effects of several parameters including nonlocal and gradient parameters, geometrical aspect ratios and substrate constants of the structure on the natural frequency and amplitude is derived. It is observed that increasing nonlocal and gradient parameters have contradictory effects of the amplitude and frequency of vibration of the laminate beam.

• Steel and Composite Structures
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• 제41권6호
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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.

• Steel and Composite Structures
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• 제32권6호
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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.

• Advances in nano research
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• 제10권2호
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• pp.115-128
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• 2021

In this article, free vibration behavior of electro-magneto-thermo sandwich Timoshenko beam made of porous core and Graphene Platelet Reinforced Composite (GPLRC) in a thermal environment is investigated. The governing equations of motion are derived by using the modified strain gradient theory for micro structures and Hamilton's principle. The magneto electro are under linear function along the thickness that contains magnetic and electric constant potentials and a cosine function. The effects of material length scale parameters, temperature change, various distributions of porous, different distributions of graphene platelets and thickness ratio on the natural frequency of Timoshenko beam are analyzed. The results show that an increase in aspect ratio, the temperature change, and the thickness of GPL leads to reduce the natural frequency; while vice versa for porous coefficient, volume fractions and length of GPL. Moreover, the effect of different size-dependent theories such as CT, MCST and MSGT on the natural frequency is investigated. It reveals that MSGT and CT have most and lowest values of natural frequency, respectively, because MSGT leads to increase the stiffness of micro Timoshenko sandwich beam by considering three material length scale parameters. It is seen that by increasing porosity coefficient, the natural frequency increases because both stiffness and mass matrices decreases, but the effect of reduction of mass matrix is more than stiffness matrix. Considering the piezo magneto-electric layers lead to enhance the stiffness of a micro beam, thus the natural frequency increases. It can be seen that with increasing of the value of WGPL, the stiffness of microbeam increases. As a result, the value of natural frequency enhances. It is shown that in hc/h = 0.7, the natural frequency for WGPL = 0.05 is 8% and 14% less than its for WGPL = 0.06 and WGPL = 0.07, respectively. The results show that with an increment in the length and width of GPLs, the natural frequency increases because the stiffness of micro structures enhances and vice versa for thickness of GPLs. It can be seen that the natural frequency for aGPL = 25 ㎛ and hc/h = 0.6 is 0.3% and 1% more than the one for aGPL = 5 ㎛ and aGPL = 1 ㎛, respectively.