Vibration Analysis of a Rotating Nanoplate Using Nonlocal Elasticity Theory

Authors

  • M Ghadiri Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
  • N Shafiei Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin, Iran
  • S Hossein Alavi School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
Abstract:

The nanostructures under rotation have high promising future to be used in nano-machines, nano-motors and nano-turbines. They are also one of the topics of interests and it is new in designing of rotating nano-systems. In this paper, the scale-dependent vibration analysis of a nanoplate with consideration of the axial force due to the rotation has been investigated. The governing equation and boundary conditions are derived using the Hamilton’s principle based on nonlocal elasticity theory. The boundary conditions of the nanoplate are considered as free-free in y direction and two clamped-free (cantilever plate) and clamped-simply (propped cantilever) in x direction. The equations have been solved using differential quadrature method to determine natural frequencies of the rotating nanoplate. For validation, in special cases, it has been shown that the obtained results coincide with literatures. The effects of the nonlocal parameter, aspect ratio, hub radius, angular velocity and different boundary conditions on the first three frequencies have been investigated. Results show that vibration behavior of the rotating nanoplate with cantilever boundary condition is different from other boundary conditions. 

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Vibration Analysis of FG Nanoplate Based on Third-Order Shear Deformation Theory (TSDT) and Nonlocal Elasticity

In present study, the third-order shear deformation theory has been developed to investigate vibration analysis of FG Nano-plates based on Eringen nonlocal elasticity theory. The materials distribution regarding to the thickness of Nano-plate has been considered based on two different models of power function and exponential function. All equations governing on the vibration of FG Nano-plate ha...

full text

Vibration Analysis of Orthotropic Triangular Nanoplates Using Nonlocal Elasticity Theory and Galerkin Method

In this article, classical plate theory (CPT) is reformulated using the nonlocal differential constitutive relations of Eringen to develop an equivalent continuum model for orthotropic triangular nanoplates. The equations of motion are derived and the Galerkin’s approach in conjunction with the area coordinates is used as a basis for the solution. Nonlocal theories are employed to bring out the...

full text

Forced vibration of piezoelectric nanowires based on nonlocal elasticity theory

In this paper, a numerical solution procedure is presented for the free and forced vibration of a piezoelectric nanowire under thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of Timoshenko beam theory. The influences of surface piezoelectricity, surface elasticity and residual surface stress are taken into consideration. Using Hamilton’s principle, t...

full text

Free Vibration Analysis of Nanoplates Made of Functionally Graded Materials Based On Nonlocal Elasticity Theory Using Finite Element Method

In this paper, an analysis of free vibration in functionally graded nanoplate is presented. Third-order shear deformation plate theory is used to reach more accuracy in results. Small-scale effects are investigated using Eringen`s nonlocal theory. The governing equations of motion are obtained by Hamilton`s principle. It is assumed that the properties of nanoplates vary through their thicknesse...

full text

forced vibration of piezoelectric nanowires based on nonlocal elasticity theory

in this paper, a numerical solution procedure is presented for the forced vibration of a piezoelectric nanowire under thermo-electro-mechanical loads based on the nonlocal elasticity theory within the framework of timoshenko beam theory. using hamilton’s principle, the nonlocal governing differential equations are derived. the governing equations and the related boundary conditions are discreti...

full text

Buckling analysis of graphene nanosheets based on nonlocal elasticity theory

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 9  issue 2

pages  319- 337

publication date 2017-06-30

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023