Vibration characteristics of circular nanoplates

Abstract

This article deals with free vibration of circular nanoplates with consideration of surface properties due to high surface to volume ratio. Classical laminated plate is employed with inclusion of surface elasticity and surface residual stress effects. Solution of the resulting differential equation leads to size dependent behavior of natural frequencies and mode shapes of vibration to be demonstrated. Deviation of the results from conventional theories is shown to be due to changes in the arguments of Bessel functions in the corresponding characteristic equations.

Surface effect on the buckling of piezoelectric nanofilms

“…However, the accurate values of surface piezoelectric and dielectric constants are not yet available due to lack of such work on piezoelectric nanomaterials. Thus the values estimated in [10] [26] and the effect of the small middle-plane strains on the elastic buckling is neglected by assuming γ ij = 0. In figure 2 the effect of shear deformation on the PNF buckling can be observed by comparing Mindlin plate theory considering shear deformation with Kirchhoff plate theory where the shearing effect is neglected.…”

“…where 1mn , 2mn and W mn are constants; and m and n are the half wave numbers. Substituting equations (24)- (26) into equations (21) and (22), and solving V from the resulting eigenvalue problem, we can obtain the buckling voltage V for a PNF as a function of (m, n). The lowest value of V gives the critical buckling voltage V cr of a PNF and associated (m, n) describes the buckling mode.…”

A general model for nano-cantilever switches with consideration of surface effects and nonlinear curvature

“…Both residual surface stress and surface elasticity effects have been incorporated in the continuum mechanical modeling of nanostructures [18,19] by using the surface elastic model provided by Gurtin and Murdoch [20] and the generalized Young-Laplace equation. The surface elastic model and generalized Young-Laplace equation have been wieldy application in investigating the influence of surface effects on the mechanical responses of nanostructures, such as nanobeams [21][22][23][24] and nanoplates [25][26][27]. Recently, some researchers investigated the pull-in instability of nano-switches with consideration of surface effects, and found that surface effects made a major contribution to the pull-in instability of electrostatically actuated nanobeams [9,[28][29][30][31].…”

Surface effect on the large amplitude periodic forced vibration of first-order shear deformable rectangular nanoplates with various edge supports

“…They included that the positive surface elastic constants lead to an increase in the critical buckling loads and natural frequencies. Assadi and Farshi [35] modified the classical Kirchhoff's circular plate model to include the effects of surface properties on the vibration characteristics of circular nanoplates. It observed that surface stress effect on the natural frequencies and mode shapes is more prominent in larger and thinner circular nanoplates.…”