Nonlinear vibration behavior of a rotating nanobeam under thermal stress using Eringen’s nonlocal elasticity and DQM

• DOI: 10.1007/s00339-016-0245-y
• Publication Date: 2016-07-09T10:14:52Z
• Authors: Navvab Shafiei; Mohammad Kazemi; Majid Ghadiri
• Keywords: Nanoelectromechanical systems; Timoshenko beam theory; Elasticity

This study is concerned with the small-scale effect on the nonlinear flapwise bending vibration of rotating cantilever and propped cantilever nanobeams. Euler–Bernoulli beam theory is used to model the nanobeam with nonlinearity. Nonlinear strain–displacement relations are employed to account for geometric nonlinearity of the system. The axial forces are modeled as the true spatial and thermal variations due to the rotation. Hamilton’s principle is used to derive the nonlinear governing equation and nonlocal nonlinear boundary conditions based on Eringen’s nonlocal elasticity theory. Finally, the differential quadrature method is used in conjunction with the direct iterative method to derive the nonlinear vibration frequencies of the nanobeam. The effects of the angular velocity, nonlocal small-scale parameter, temperature change and nonlinear amplitude on nonlinear vibration of the rotary nanobeam are discussed. The results of this work can be used in nanosensors, nanomotors, nanoturbines and NEMS applications.