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A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams

  • Bouafia, Khadra (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes) ;
  • Kaci, Abdelhakim (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil) ;
  • Houari, Mohammed Sid Ahmed (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes, Faculte de Technologie, Departement de genie civil) ;
  • Benzair, Abdelnour (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes)
  • Received : 2016.02.03
  • Accepted : 2016.10.07
  • Published : 2017.02.25
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Abstract

In this paper, size dependent bending and free flexural vibration behaviors of functionally graded (FG) nanobeams are investigated using a nonlocal quasi-3D theory in which both shear deformation and thickness stretching effects are introduced. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanostructures. The present theory incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and furthermore accounts for both shear deformation and thickness stretching effects by virtue of a hyperbolic variation of all displacements through the thickness without using shear correction factor. The material properties of FG nanobeams are assumed to vary through the thickness according to a power law. The neutral surface position for such FG nanobeams is determined and the present theory based on exact neutral surface position is employed here. The governing equations are derived using the principal of minimum total potential energy. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and dynamic responses of the FG nanobeam are discussed in detail. A detailed numerical study is carried out to examine the effect of material gradient index, the nonlocal parameter, the beam aspect ratio on the global response of the FG nanobeam. These findings are important in mechanical design considerations of devices that use carbon nanotubes.

Keywords

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  122. Participation Factor and Vibration of Carbon Nanotube with Vacancies vol.57, pp.None, 2017, https://doi.org/10.4028/www.scientific.net/jnanor.57.158
  123. A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams vol.57, pp.None, 2017, https://doi.org/10.4028/www.scientific.net/jnanor.57.175
  124. Buckling behavior of rectangular plates under uniaxial and biaxial compression vol.70, pp.1, 2019, https://doi.org/10.12989/sem.2019.70.1.113
  125. A simple HSDT for bending, buckling and dynamic behavior of laminated composite plates vol.70, pp.3, 2019, https://doi.org/10.12989/sem.2019.70.3.325
  126. Dynamic analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT vol.7, pp.3, 2017, https://doi.org/10.12989/anr.2019.7.3.191
  127. Effect of distribution shape of the porosity on the interfacial stresses of the FGM beam strengthened with FRP plate vol.16, pp.5, 2017, https://doi.org/10.12989/eas.2019.16.5.601
  128. Influence of shear preload on wave propagation in small-scale plates with nanofibers vol.70, pp.4, 2017, https://doi.org/10.12989/sem.2019.70.4.407
  129. The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate vol.18, pp.2, 2017, https://doi.org/10.12989/gae.2019.18.2.161
  130. A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation vol.31, pp.5, 2017, https://doi.org/10.12989/scs.2019.31.5.503
  131. Conformable solution of fractional vibration problem of plate subjected to in-plane loads vol.28, pp.6, 2019, https://doi.org/10.12989/was.2019.28.6.347
  132. Stability analysis of embedded graphene platelets reinforced composite plates in thermal environment vol.134, pp.7, 2019, https://doi.org/10.1140/epjp/i2019-12581-6
  133. Vibration characteristics of zigzag and chiral functionally graded material rotating carbon nanotubes sandwich with ring supports vol.233, pp.16, 2017, https://doi.org/10.1177/0954406219855095
  134. Nonlocal Buckling Analysis of Composite Curved Beams Reinforced with Functionally Graded Carbon Nanotubes vol.24, pp.15, 2017, https://doi.org/10.3390/molecules24152750
  135. Free Vibration Analysis of Triclinic Nanobeams Based on the Differential Quadrature Method vol.9, pp.17, 2017, https://doi.org/10.3390/app9173517
  136. Analyzing nonlinear mechanical-thermal buckling of imperfect micro-scale beam made of graded graphene reinforced composites vol.8, pp.3, 2017, https://doi.org/10.12989/amr.2019.8.3.219
  137. Analyzing large-amplitude vibration of nonlocal beams made of different piezo-electric materials in thermal environment vol.8, pp.3, 2019, https://doi.org/10.12989/amr.2019.8.3.237
  138. Size-dependent vibration analysis of laminated composite plates vol.7, pp.5, 2017, https://doi.org/10.12989/anr.2019.7.5.337
  139. Vibration analysis of nonlocal porous nanobeams made of functionally graded material vol.7, pp.5, 2019, https://doi.org/10.12989/anr.2019.7.5.351
  140. Nonlinear forced vibrations of sandwich smart nanobeams with two-phase piezo-magnetic face sheets vol.134, pp.10, 2019, https://doi.org/10.1140/epjp/i2019-12806-8
  141. Frequency response of initially deflected nanotubes conveying fluid via a nonlinear NSGT model vol.72, pp.1, 2017, https://doi.org/10.12989/sem.2019.72.1.071
  142. Assessment of porosity influence on dynamic characteristics of smart heterogeneous magneto-electro-elastic plates vol.72, pp.1, 2019, https://doi.org/10.12989/sem.2019.72.1.113
  143. Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT vol.24, pp.4, 2017, https://doi.org/10.12989/cac.2019.24.4.347
  144. A Non-Linear Spring Model for Predicting Modal Behavior of Oscillators Built from Double Walled Carbon Nanotubes vol.60, pp.None, 2017, https://doi.org/10.4028/www.scientific.net/jnanor.60.21
  145. A Non-Linear Spring Model for Predicting Modal Behavior of Oscillators Built from Double Walled Carbon Nanotubes vol.60, pp.None, 2017, https://doi.org/10.4028/www.scientific.net/jnanor.60.21
  146. The nano scale bending and dynamic properties of isolated protein microtubules based on modified strain gradient theory vol.7, pp.6, 2017, https://doi.org/10.12989/anr.2019.7.6.443
  147. Dynamic modeling of a multi-scale sandwich composite panel containing flexible core and MR smart layer vol.134, pp.12, 2017, https://doi.org/10.1140/epjp/i2019-12662-6
  148. A new higher-order shear and normal deformation theory for the buckling analysis of new type of FGM sandwich plates vol.72, pp.5, 2019, https://doi.org/10.12989/sem.2019.72.5.653
  149. On the modeling of dynamic behavior of composite plates using a simple nth-HSDT vol.29, pp.6, 2017, https://doi.org/10.12989/was.2019.29.6.371
  150. Transfer matrix formulations and single variable shear deformation theory for crack detection in beam-like structures vol.73, pp.2, 2020, https://doi.org/10.12989/sem.2020.73.2.109
  151. Hygrothermal postbuckling analysis of smart multiscale piezoelectric composite shells vol.135, pp.2, 2017, https://doi.org/10.1140/epjp/s13360-020-00137-w
  152. A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates vol.25, pp.2, 2020, https://doi.org/10.12989/sss.2020.25.2.197
  153. A numerical method for dynamic characteristics of nonlocal porous metal-ceramic plates under periodic dynamic loads vol.7, pp.1, 2020, https://doi.org/10.12989/smm.2020.7.1.027
  154. Buckling response of smart plates reinforced by nanoparticles utilizing analytical method vol.35, pp.1, 2020, https://doi.org/10.12989/scs.2020.35.1.001
  155. A refined HSDT for bending and dynamic analysis of FGM plates vol.74, pp.1, 2020, https://doi.org/10.12989/sem.2020.74.1.105
  156. Bending analysis of magneto-electro piezoelectric nanobeams system under hygro-thermal loading vol.8, pp.3, 2017, https://doi.org/10.12989/anr.2020.8.3.203
  157. Buckling and free vibration analyses of nanobeams with surface effects via various higher-order shear deformation theories vol.74, pp.2, 2020, https://doi.org/10.12989/sem.2020.74.2.175
  158. Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory vol.25, pp.4, 2017, https://doi.org/10.12989/sss.2020.25.4.409
  159. Two new indices for structural optimization of free vibration suppression vol.61, pp.5, 2020, https://doi.org/10.1007/s00158-019-02451-z
  160. Nonlinear vibration of smart nonlocal magneto-electro-elastic beams resting on nonlinear elastic substrate with geometrical imperfection and various piezoelectric effects vol.25, pp.5, 2017, https://doi.org/10.12989/sss.2020.25.5.619
  161. Nonlinear vibration of smart nonlocal magneto-electro-elastic beams resting on nonlinear elastic substrate with geometrical imperfection and various piezoelectric effects vol.25, pp.5, 2017, https://doi.org/10.12989/sss.2020.25.5.619
  162. Vibration analysis of nonlocal strain gradient porous FG composite plates coupled by visco-elastic foundation based on DQM vol.9, pp.3, 2020, https://doi.org/10.12989/csm.2020.9.3.201
  163. Mixture rule for studding the environmental pollution reduction in concrete structures containing nanoparticles vol.9, pp.3, 2017, https://doi.org/10.12989/csm.2020.9.3.281
  164. Dynamic behavior of axially functionally graded simply supported beams vol.25, pp.6, 2017, https://doi.org/10.12989/sss.2020.25.6.669
  165. Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes vol.36, pp.6, 2017, https://doi.org/10.12989/scs.2020.36.6.643
  166. Dynamics of graphene-nanoplatelets reinforced composite nanoplates including different boundary conditions vol.36, pp.6, 2017, https://doi.org/10.12989/scs.2020.36.6.689
  167. Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam vol.26, pp.3, 2017, https://doi.org/10.12989/sss.2020.26.3.361
  168. Wave dispersion characteristics of fluid-conveying magneto-electro-elastic nanotubes vol.36, pp.4, 2017, https://doi.org/10.1007/s00366-019-00790-5
  169. Buckling Analysis of CNTRC Curved Sandwich Nanobeams in Thermal Environment vol.11, pp.7, 2017, https://doi.org/10.3390/app11073250
  170. Wave dispersion of nanobeams incorporating stretching effect vol.31, pp.4, 2017, https://doi.org/10.1080/17455030.2019.1607623
  171. Mechanical analysis of bi-functionally graded sandwich nanobeams vol.11, pp.1, 2017, https://doi.org/10.12989/anr.2021.11.1.055
  172. Mass density effect on vibration of zigzag and chiral SWCNTs: A theoretical study vol.23, pp.6, 2017, https://doi.org/10.1177/1099636220906257