Kirchhoff Plate Theory

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Zhibin Shen - One of the best experts on this subject based on the ideXlab platform.

  • vibration analysis of a single layered graphene sheet based mass sensor using the galerkin strip distributed transfer function method
    Acta Mechanica, 2016
    Co-Authors: Renwei Jiang, Zhibin Shen, Guojin Tang
    Abstract:

    The free vibration of a single-layered graphene sheet (SLGS)-based mass sensor is analyzed using the Galerkin strip distributed transfer function method (GSDTFM) based on the nonlocal Kirchhoff Plate Theory. The dynamic equations of the SLGS-based mass sensor are formulated, and the semi-analytical solutions of the frequency shift are computed with the GSDTFM. The effects of the nonlocal parameter, the attached nanoparticle locations, the Plate side length, as well as the boundary conditions, on the frequency shift are studied. The simulated results show that the frequency shift of the SLGS-based mass sensor becomes smaller when the nonlocal parameter increases. The SLGS-based mass sensor is more sensitive when the attached nanoparticle is closer to the SLGS center or the side length of the SLGS becomes smaller. The boundary conditions strongly affect the frequency shift. Stiffer boundary condition causes larger frequency shift.

  • transverse vibration of circular graphene sheet based mass sensor via nonlocal Kirchhoff Plate Theory
    Computational Materials Science, 2014
    Co-Authors: Shiming Zhou, Liping Sheng, Zhibin Shen
    Abstract:

    Abstract The potential of circular graphene sheet (GS) as a mass sensor is explored. A circular GS carrying a nanoparticle at an arbitrary position is modeled as a circular nanoPlate with a concentrated micro-mass for clamped and simply supported boundary conditions. Based on the nonlocal Kirchhoff Plate Theory which incorporates size effects into the classical Theory, the natural frequencies of the mass sensor are derived using the Galerkin method. The effects of mass and position of the nanoparticle on the frequencies and frequency shifts are discussed. The frequencies reduce to the results of the classical model for the absence of the small scale effect, which maintain in accordance with those available in literatures. Numerical results show that when the mass of the attached nanoparticle increases or its location is closer to the Plate center, the natural frequency decreases, but frequency shift increases. Small scale effect diminishes the frequencies strongly, but has less effect on the frequency shifts. When the radius of the nanoPlate decreases, the frequency shift increases. The results are helpful to design circular GS-based resonators as nanomechanical mass sensor.

  • vibration of single layered graphene sheet based nanomechanical sensor via nonlocal Kirchhoff Plate Theory
    Computational Materials Science, 2012
    Co-Authors: Zhibin Shen, Haili Tang, Daokui Li, Guojin Tang
    Abstract:

    Abstract The potential of single-layered graphene sheet (SLGS) as a nanomechanical sensor is explored. A simply supported SLGS carrying a nanoparticle at any position is modeled as a rectangular nanoPlate with a concentrated micro-mass. Based on the nonlocal Kirchhoff Theory of Plates which incorporates size effects into the classical Theory, the natural frequencies of a nanomechanical sensor are derived using the Galerkin method. The effects of the mass and position of the nanoparticle on the frequency shift are discussed. In the absence of the nonlocal parameter, the frequencies reduce to the results of the classical model, in agreement with those using the finite element method. The obtained results show that when the mass of the attached nanoparticle increases or its location is closer to the Plate center, the natural frequency decreases, but frequency shift increases. Small scale effect diminishes the frequency shift. Decreasing the Plate side length also increases the frequency shift. Obtained results are helpful to the design of SLGS-based resonator as nanomechanical mass sensor.

Guojin Tang - One of the best experts on this subject based on the ideXlab platform.

  • A semi-analytical method for nonlocal buckling and vibration of a single-layered graphene sheet nanomechanical resonator subjected to initial in-plane loads
    Acta Mechanica, 2017
    Co-Authors: Renwei Jiang, Zhi Bin Shen, Guojin Tang
    Abstract:

    A semi-analytical method named Galerkin strip distributed transfer function method (GSDTFM) is employed to solve the buckling and vibration of a single-layered graphene sheet (SLGS) nanomechanical resonator subjected to initial in-plane loads within the framework of the nonlocal Kirchhoff Plate Theory. The buckling load and the frequency shift are obtained by using the GSDTFM. And the effects of the initial in-plane load, the nonlocal parameter as well as the attached nanoparticle location on the frequency shift are investigated. The simulated results show that the buckling load of the SLGS depends on not only the side length of the SLGS, but also the small scale effects. The impact of the initial in-plane load on the fundamental frequency is significant. The frequency shift at an initial tensile load is larger than that at an initial compressive load. These results are consistent with the previously reported ones.

  • vibration analysis of a single layered graphene sheet based mass sensor using the galerkin strip distributed transfer function method
    Acta Mechanica, 2016
    Co-Authors: Renwei Jiang, Zhibin Shen, Guojin Tang
    Abstract:

    The free vibration of a single-layered graphene sheet (SLGS)-based mass sensor is analyzed using the Galerkin strip distributed transfer function method (GSDTFM) based on the nonlocal Kirchhoff Plate Theory. The dynamic equations of the SLGS-based mass sensor are formulated, and the semi-analytical solutions of the frequency shift are computed with the GSDTFM. The effects of the nonlocal parameter, the attached nanoparticle locations, the Plate side length, as well as the boundary conditions, on the frequency shift are studied. The simulated results show that the frequency shift of the SLGS-based mass sensor becomes smaller when the nonlocal parameter increases. The SLGS-based mass sensor is more sensitive when the attached nanoparticle is closer to the SLGS center or the side length of the SLGS becomes smaller. The boundary conditions strongly affect the frequency shift. Stiffer boundary condition causes larger frequency shift.

  • vibration of single layered graphene sheet based nanomechanical sensor via nonlocal Kirchhoff Plate Theory
    Computational Materials Science, 2012
    Co-Authors: Zhibin Shen, Haili Tang, Daokui Li, Guojin Tang
    Abstract:

    Abstract The potential of single-layered graphene sheet (SLGS) as a nanomechanical sensor is explored. A simply supported SLGS carrying a nanoparticle at any position is modeled as a rectangular nanoPlate with a concentrated micro-mass. Based on the nonlocal Kirchhoff Theory of Plates which incorporates size effects into the classical Theory, the natural frequencies of a nanomechanical sensor are derived using the Galerkin method. The effects of the mass and position of the nanoparticle on the frequency shift are discussed. In the absence of the nonlocal parameter, the frequencies reduce to the results of the classical model, in agreement with those using the finite element method. The obtained results show that when the mass of the attached nanoparticle increases or its location is closer to the Plate center, the natural frequency decreases, but frequency shift increases. Small scale effect diminishes the frequency shift. Decreasing the Plate side length also increases the frequency shift. Obtained results are helpful to the design of SLGS-based resonator as nanomechanical mass sensor.

Maziar Janghorban - One of the best experts on this subject based on the ideXlab platform.

  • resonance behavior of fg rectangular micro nano Plate based on nonlocal elasticity Theory and strain gradient Theory with one gradient constant
    Composite Structures, 2014
    Co-Authors: Mohammad Rahim Nami, Maziar Janghorban
    Abstract:

    Abstract In this article, for the first time, the resonance behaviors of functionally graded micro/nano Plates are presented using Kirchhoff Plate Theory. To consider the small scale effects, the nonlocal elasticity Theory and strain gradient Theory with one gradient parameter are adopted. In this work, one can see the different behaviors of these two theories. To solve the governing equations, an analytical approach is used to investigate simply supported functionally graded rectangular micro Plates. To show the accuracy of present methodology, our results are compared with the results for isotropic gradient micro Plate. The effects of gradient parameter, aspect ratio and nonlocal parameter are also studied.

  • Resonance behavior of FG rectangular micro/nano Plate based on nonlocal elasticity Theory and strain gradient Theory with one gradient constant
    Composite Structures, 2014
    Co-Authors: Mohammad Rahim Nami, Maziar Janghorban
    Abstract:

    Abstract In this article, for the first time, the resonance behaviors of functionally graded micro/nano Plates are presented using Kirchhoff Plate Theory. To consider the small scale effects, the nonlocal elasticity Theory and strain gradient Theory with one gradient parameter are adopted. In this work, one can see the different behaviors of these two theories. To solve the governing equations, an analytical approach is used to investigate simply supported functionally graded rectangular micro Plates. To show the accuracy of present methodology, our results are compared with the results for isotropic gradient micro Plate. The effects of gradient parameter, aspect ratio and nonlocal parameter are also studied.

Liying Jiang - One of the best experts on this subject based on the ideXlab platform.

  • flexoelectric effect on the electroelastic responses and vibrational behaviors of a piezoelectric nanoPlate
    Journal of Applied Physics, 2014
    Co-Authors: Zhengrong Zhang, Zhi Yan, Liying Jiang
    Abstract:

    Flexoelectricity, referring to the coupling between electric polarization and strain gradients, is a universal effect in all dielectrics and may become manifest at the nano-scale. The current work aims to investigate the flexoelectric effect on the electroelastic responses and the free vibrational behaviors of a piezoelectric nanoPlate (PNP). Based on the conventional Kirchhoff Plate Theory and the extended linear piezoelectricity Theory, the governing equation and the boundary conditions of a clamped PNP with the consideration of the static bulk flexoelectricity are derived. Ritz approximate solutions of the electroelastic fields and the resonant frequencies demonstrate the size-dependency of the flexoelectric effect, which is more prominent for thinner Plates with smaller thickness as expected. Simulation results also indicate that the influence of the flexoelectricity upon the electroelastic fields of a bending PNP and the transverse vibration of the PNP is sensitive to the Plate in-plane dimensions as...

  • Surface effects on the vibration and buckling of piezoelectric nanoPlates
    EPL (Europhysics Letters), 2012
    Co-Authors: Zhi Yan, Liying Jiang
    Abstract:

    In this letter, surface effects on the vibration and buckling of a clamped-clamped piezoelectric nanoPlate (PNP) are investigated by using Kirchhoff Plate Theory with the incorporation of the surface piezoelectricity model and the generalized Young-Laplace equations. Ritz solutions show that the surface effects on the resonant frequency are more prominent for the PNPs with smaller thickness and larger aspect ratio, with dominant effect from surface piezoelectricity and residual surface stress. Results also suggest potential for frequency tuning of the PNPs via applied electric potentials. Simulation results on the critical buckling potential indicate that the influence of the combined surface effects is the competition between the residual surface stress and surface piezoelectricity. This work is helpful for the characterization of the mechanical properties and design of PNP-based devices.

  • Surface effects on the electroelastic responses of a thin piezoelectric Plate with nanoscale thickness
    Journal of Physics D: Applied Physics, 2012
    Co-Authors: Zhi Yan, Liying Jiang
    Abstract:

    This work aims to investigate the electroelastic responses of a thin piezoelectric Plate under mechanical and electrical loads with the consideration of surface effects. Surface effects, including surface elasticity, residual surface stress and surface piezoelectricity, are incorporated into the conventional Kirchhoff Plate Theory for a piezoelectric Plate via the surface piezoelectricity model and the generalized Young–Laplace equations. Different from the results predicted by the conventional Plate Theory ignoring the surface effects, the proposed model predicts size-dependent behaviours of the piezoelectric thin Plate with nanoscale thickness. It is found that surface effects have significant influence on the electroelastic responses of the piezoelectric nanoPlate. This work is expected to provide more accurate predictions on characterizing nanofilm or nanoribbon based piezoelectric devices in nanoelectromechanical systems.

Mohammad Rahim Nami - One of the best experts on this subject based on the ideXlab platform.

  • resonance behavior of fg rectangular micro nano Plate based on nonlocal elasticity Theory and strain gradient Theory with one gradient constant
    Composite Structures, 2014
    Co-Authors: Mohammad Rahim Nami, Maziar Janghorban
    Abstract:

    Abstract In this article, for the first time, the resonance behaviors of functionally graded micro/nano Plates are presented using Kirchhoff Plate Theory. To consider the small scale effects, the nonlocal elasticity Theory and strain gradient Theory with one gradient parameter are adopted. In this work, one can see the different behaviors of these two theories. To solve the governing equations, an analytical approach is used to investigate simply supported functionally graded rectangular micro Plates. To show the accuracy of present methodology, our results are compared with the results for isotropic gradient micro Plate. The effects of gradient parameter, aspect ratio and nonlocal parameter are also studied.

  • Resonance behavior of FG rectangular micro/nano Plate based on nonlocal elasticity Theory and strain gradient Theory with one gradient constant
    Composite Structures, 2014
    Co-Authors: Mohammad Rahim Nami, Maziar Janghorban
    Abstract:

    Abstract In this article, for the first time, the resonance behaviors of functionally graded micro/nano Plates are presented using Kirchhoff Plate Theory. To consider the small scale effects, the nonlocal elasticity Theory and strain gradient Theory with one gradient parameter are adopted. In this work, one can see the different behaviors of these two theories. To solve the governing equations, an analytical approach is used to investigate simply supported functionally graded rectangular micro Plates. To show the accuracy of present methodology, our results are compared with the results for isotropic gradient micro Plate. The effects of gradient parameter, aspect ratio and nonlocal parameter are also studied.