Uncertainty modeling for vibration and buckling behaviors of functionally graded nanobeams in thermal environment

Uncertainty modeling for vibration and buckling behaviors of functionally graded nanobeams in... High accuracy modeling of nanostructure is a crucial issue in nano electromechanical systems. This study investigates the effect of nanomaterial uncertainties on vibration and buckling behaviors of functionally graded (FG) nanobeams in thermal environment. The size-dependent governing differential equation is derived based on the nonlocal Euler–Bernoulli beam theory with the thermal effect and the analytical formulations of the natural frequencies are deduced. To avoid the shortcoming of probabilistic method in the case of inadequate data, a non-probabilistic uncertainty modeling for the FG nanobeams is developed by quantifying nanomaterial uncertainties as interval parameters. Meanwhile, a hull iterative algorithm (HIA) for solving this model is presented to evaluate the bounds of the natural frequencies. After validation of HIA by comparing with Monte Carlo simulation and sensitivity based interval analysis method, the detailed parametric study is performed to understand the combined influences of nanomaterial uncertainties and size-dependent parameter, power-law index as well as temperature change on the natural frequencies. Additionally, the lower bound of the critical buckling temperature is discussed under different size-dependent parameters and power-law indices. The bounds of the natural frequencies and the critical buckling temperature obtained here are helpful for the safety and optimal design of nano electromechanical systems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Composite Structures Elsevier

Uncertainty modeling for vibration and buckling behaviors of functionally graded nanobeams in thermal environment

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Publisher
Elsevier
Copyright
Copyright © 2017 Elsevier Ltd
ISSN
0263-8223
eISSN
1879-1085
D.O.I.
10.1016/j.compstruct.2017.10.053
Publisher site
See Article on Publisher Site

Abstract

High accuracy modeling of nanostructure is a crucial issue in nano electromechanical systems. This study investigates the effect of nanomaterial uncertainties on vibration and buckling behaviors of functionally graded (FG) nanobeams in thermal environment. The size-dependent governing differential equation is derived based on the nonlocal Euler–Bernoulli beam theory with the thermal effect and the analytical formulations of the natural frequencies are deduced. To avoid the shortcoming of probabilistic method in the case of inadequate data, a non-probabilistic uncertainty modeling for the FG nanobeams is developed by quantifying nanomaterial uncertainties as interval parameters. Meanwhile, a hull iterative algorithm (HIA) for solving this model is presented to evaluate the bounds of the natural frequencies. After validation of HIA by comparing with Monte Carlo simulation and sensitivity based interval analysis method, the detailed parametric study is performed to understand the combined influences of nanomaterial uncertainties and size-dependent parameter, power-law index as well as temperature change on the natural frequencies. Additionally, the lower bound of the critical buckling temperature is discussed under different size-dependent parameters and power-law indices. The bounds of the natural frequencies and the critical buckling temperature obtained here are helpful for the safety and optimal design of nano electromechanical systems.

Journal

Composite StructuresElsevier

Published: Jan 15, 2018

References

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