• Title, Summary, Keyword: porous nanoplate

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Nonlinear bending analysis of porous FG thick annular/circular nanoplate based on modified couple stress and two-variable shear deformation theory using GDQM

  • Sadoughifar, Amirmahmoud;Farhatnia, Fatemeh;Izadinia, Mohsen;Talaeitaba, Sayed Behzad
    • Steel and Composite Structures
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    • v.33 no.2
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    • pp.307-318
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    • 2019
  • This is the first attempt to consider the nonlinear bending analysis of porous functionally graded (FG) thick annular and circular nanoplates resting on Kerr foundation. The size effects are captured based on modified couple stress theory (MCST). The material properties of the porous FG nanostructure are assumed to vary smoothly through the thickness according to a power law distribution of the volume fraction of the constituent materials. The elastic medium is modeled by Kerr elastic foundation which consists of two spring layers and one shear layer. The governing equations are extracted based on Hamilton's principle and two variables refined plate theory. Utilizing generalized differential quadrature method (GDQM), the nonlinear static behavior of the nanostructure is obtained under different boundary conditions. The effects of various parameters such as material length scale parameter, boundary conditions, and geometrical parameters of the nanoplate, elastic medium constants, porosity and FG index are shown on the nonlinear deflection of the annular and circular nanoplates. The results indicate that with increasing the material length scale parameter, the nonlinear deflection is decreased. In addition, the dimensionless nonlinear deflection of the porous annular nanoplate is diminished with the increase of porosity parameter. It is hoped that the present work may provide a benchmark in the study of nonlinear static behavior of porous nanoplates.

Size-dependent buckling behaviour of FG annular/circular thick nanoplates with porosities resting on Kerr foundation based on new hyperbolic shear deformation theory

  • Sadoughifar, Amirmahmoud;Farhatnia, Fatemeh;Izadinia, Mohsen;Talaeetaba, Sayed Behzad
    • 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.

Nonlinear vibration analysis of the viscoelastic composite nanoplate with three directionally imperfect porous FG core

  • Mohammadia, M.;Rastgoo, A.
    • Structural Engineering and Mechanics
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    • v.69 no.2
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    • pp.131-143
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    • 2019
  • In this study, the nonlinear vibration analysis of the composite nanoplate is studied. The composite nanoplate is fabricated by the functional graded (FG) core and lipid face sheets. The material properties in the FG core vary in three directions. The Kelvin-Voigt model is used to study the viscoelastic effect of the lipid layers. By using the Von-Karman assumptions, the nonlinear differential equation of the vibration analysis of the composite nanoplate is obtained. The foundation of the system is modeled by the nonlinear Pasternak foundation. The Bubnov-Galerkin method and the multiple scale method are used to solve the nonlinear differential equation of the composite nanoplate. The free and force vibration analysis of the composite nanoplate are studied. A comparison between the presented results and the reported results is done and good achievement is obtained. The reported results are verified by the results which are obtained by the Runge-Kutta method. The effects of different parameters on the nonlinear vibration frequencies, the primary, the super harmonic and subharmonic resonance cases are investigated. This work will be useful to design the nanosensors with high biocompatibility.

Nonlocal strain gradient model for thermal stability of FG nanoplates integrated with piezoelectric layers

  • Karami, Behrouz;Shahsavari, Davood
    • Smart Structures and Systems
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    • v.23 no.3
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    • pp.215-225
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    • 2019
  • In the present paper, the nonlocal strain gradient refined model is used to study the thermal stability of sandwich nanoplates integrated with piezoelectric layers for the first time. The influence of Kerr elastic foundation is also studied. The present model incorporates two small-scale coefficients to examine the size-dependent thermal stability response. Elastic properties of nanoplate made of functionally graded materials (FGMs) are supposed to vary through the thickness direction and are estimated employing a modified power-law rule in which the porosity with even type of distribution is approximated. The governing differential equations of embedded sandwich piezoelectric porous nanoplates under hygrothermal loading are derived through Hamilton's principle where the Galerkin method is applied to solve the stability problem of the nanoplates with simply-supported edges. It is indicated that the thermal stability characteristics of the porous nanoplates are obviously influenced by the porosity volume fraction and material variation, nonlocal parameter, strain gradient parameter, geometry of the nanoplate, external voltage, temperature and humidity variations, and elastic foundation parameters.

Dispersion of waves in FG porous nanoscale plates based on NSGT in thermal environment

  • Ebrahimi, Farzad;Seyfi, Ali;Dabbagh, Ali
    • Advances in nano research
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    • v.7 no.5
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    • pp.325-335
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    • 2019
  • In the present study, nonlocal strain gradient theory (NSGT) is developed for wave propagation of functionally graded (FG) nanoscale plate in the thermal environment by considering the porosity effect. $Si_3N_4$ as ceramic phase and SUS304 as metal phase are regarded to be constitutive material of FG nanoplate. The porosity effect is taken into account on the basis of the newly extended method which considers coupling influence between Young's modulus and mass density. The motion relation is derived by applying Hamilton's principle. NSGT is implemented in order to account for small size effect. Wave frequency and phase velocity are obtained by solving the problem via an analytical method. The effects of different parameters such as porosity coefficient, gradient index, wave number, scale factor and temperature change on phase velocity and wave frequency of FG porous nanoplate have been examined and been presented in a group of illustrations.

Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and non-uniform porosities

  • Fenjan, Raad M.;Ahmed, Ridha A.;Alasadi, Abbas A.;Faleh, Nadhim M.
    • Coupled systems mechanics
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    • v.8 no.3
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    • pp.247-257
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    • 2019
  • Fee vibrational characteristics of porous steel double-coupled nanoplate system in thermo-elastic medium is studied via a refined plate model. Different pore dispersions called uniform, symmetric and asymmetric have been defined. Nonlocal strain gradient theory (NSGT) containing two scale parameters has been adopted to stablish size-dependent modeling of the system. Hamilton's principle has been adopted to stablish the governing equations. Obtained results from Galerkin's method are verified with those provided in the literature. The effects of nonlocal parameter, strain gradient, foundation parameters, porosity distributions and porosity coefficient on vibration frequencies of metal foam nanoscale plates have been examined.

A numerical method for dynamic characteristics of nonlocal porous metal-ceramic plates under periodic dynamic loads

  • Abdulrazzaq, Mohammed Abdulraoof;Kadhim, Zeyad D.;Faleh, Nadhim M.;Moustafa, Nader M.
    • Structural Monitoring and Maintenance
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    • v.7 no.1
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    • pp.27-42
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    • 2020
  • Dynamic stability of graded nonlocal nano-dimension plates on elastic substrate due to in-plane periodic loads has been researched via a novel 3- unknown plate theory based on exact position of neutral surface. Proposed theory confirms the shear deformation effects and contains lower field components in comparison to first order and refined 4- unknown plate theories. A modified power-law function has been utilized in order to express the porosity-dependent material coefficients. The equations of nanoplate have been represented in the context of Mathieu-Hill equations and Chebyshev-Ritz-Bolotin's approach has been performed to derive the stability boundaries. Detailed impacts of static/dynamic loading parameters, nonlocal constant, foundation parameters, material index and porosities on instability boundaries of graded nanoscale plates are researched.

Mechanical-hygro-thermal vibrations of functionally graded porous plates with nonlocal and strain gradient effects

  • Fenjan, Raad M.;Hamad, Luay Badr;Faleh, Nadhim M.
    • Advances in aircraft and spacecraft science
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    • v.7 no.2
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    • pp.169-186
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    • 2020
  • Based upon differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), mechanical-hygro-thermal vibrational analyzes of shear deformable porous functionally graded (FG) nanoplate on visco-elastic medium has been performed. The presented formulation incorporates two scale factors for examining vibrational behaviors of nano-dimension plates more accurately. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. It is supposed that the nano-size plate is exposed to hygro-thermal and variable compressive mechanical loadings. The governing equations achieved by Hamilton's principle are solved implementing DQM. Presented results indicate the prominence of moisture/temperature variation, damping factor, material gradient index, nonlocal coefficient, strain gradient coefficient and porosities on vibrational frequencies of FG nano-size plate.

Nonlocal-strain gradient forced vibration analysis of metal foam nanoplates with uniform and graded porosities

  • Barati, Mohammad Reza
    • Advances in nano research
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    • v.5 no.4
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    • pp.393-414
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    • 2017
  • Forced vibration behavior of porous metal foam nanoplates on elastic medium is studied via a 4-variable plate theory. Different porosity distributions called uniform, symmetric and asymmetric are considered. Nonlocal strain gradient theory (NSGT) containing two scale parameters is employed for size-dependent modeling of porous nanoplates. The present plate theory satisfies the shear deformation effect and it has lower field variables compared with first order plate theory. Hamilton's principle is employed to derive the governing equations. Obtained results from Galerkin's method are verified with those provided in the literature. The effects of nonlocal parameter, strain gradient, foundation parameters, dynamic loading, porosity distributions and porosity coefficient on dynamic deflection and resonance frequencies of metal foam nanoscale plates are examined.

Investigating dynamic stability of metal foam nanoplates under periodic in-plane loads via a three-unknown plate theory

  • Fenjan, Raad M.;Ahmed, Ridha A.;Faleh, Nadhim M.
    • Advances in aircraft and spacecraft science
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    • v.6 no.4
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    • pp.297-314
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    • 2019
  • Dynamic stability of a porous metal foam nano-dimension plate on elastic substrate exposed to bi-axial time-dependent forces has been studied via a novel 3-variable plate theory. Various pore contents based on uniform and non-uniform models have been introduced. The presented plate model contains smaller number of field variables with shear deformation verification. Hamilton's principle will be utilized to deduce the governing equations. Next, the equations have been defined in the context of Mathieu-Hill equation. Correctness of presented methodology has been verified by comparison of derived results with previous data. Impacts of static and dynamical force coefficients, non-local coefficient, foundation coefficients, pore distributions and boundary edges on stability regions of metal foam nanoscale plates will be studied.