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

摘要

AbstractHigh 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.