Abstract
Small scale parameter of graphene sheet is considered as uncertain one, vibration equation of a simply supported graphene sheet with uncertainty is established based on nonlocal theory. Trigonometric function series solution and interval operator are used to obtain the upper and lower bound of response of the simply supported graphene sheet. the uncertainty level of response for the different dimension is investigated. The numerical result shows that for the same uncertainty level of small scale parameter, the uncertainty level of the response will decrease with increase of the graphene sheet dimension, and a small uncertainty level of the small scale parameter can cause much greater uncertainty level of the response before the small scale effect disappears.
Highlights
With the development of nano mechanical and electrical technology, the mechanical properties of nanoscale structures to cause the considerable attention of many scholars
Small scale parameter of graphene sheet is considered as uncertain one, vibration equation of a supported graphene sheet with uncertainty is established based on nonlocal theory
The numerical result shows that for the same uncertainty level of small scale parameter, the uncertainty level of the response will decrease with increase of the graphene sheet dimension, and a small uncertainty level of the small scale parameter can cause much greater uncertainty level of the response before the small scale effect disappears
Summary
With the development of nano mechanical and electrical technology, the mechanical properties of nanoscale structures to cause the considerable attention of many scholars. Based on the nonlocal theory, Zhang, Liu, and Wang [2] studied the buckling of multi-walled carbon nanotube. Han, and Long [3,4,5] investigated the small scale effect and the vibration of carbon nanotube. L Yang,J S Peng [9] used the nonlocal-gradient elasticity theory to scale effect on dynamic analysis of electrostatically actuated nano beams. P., et al [11] carried out nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory. Until now, the deterministic small scale parameter of the graphene sheet has been given. A nonlocal model of nanoplate is developed for vibration of a supported graphene sheet with uncertainty. VIBRATION OF A SUPPORTED GRAPHENE SHEET WITH UNCERTAIN SMALL SCALE PARAMETER BASED ON NONLOCAL THEORY.
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