Dynamic Stability of Nanobeams Based on the Reddy's Beam Theory

The dynamic stability of nanobeams has been investigated by the Euler-Bernoulli and Timoshenko beam theories in the literature, but the higher-order Reddy beam theory has not been applied in the dynamic stability evaluation of nanobeams. In this work, the governing equations of the motion and dynamic stability of a nanobeam embedded in elastic medium are derived based on the nonlocal theory and the Reddy's beam theory. The parametric studies indicate that the principal instability region (PIR) moves to a lower frequency zone when length, sectional height, nonlocal parameter, Young's modulus and mass density of the Reddy nanobeam increase. The PIR shifts to a higher frequency zone only under increasing shear modulus. Increase in length makes the width of the PIR shrink obviously, while increase in height and Young's modulus makes the width of the PIR enlarge. The sectional width and foundation modulus have few effects on PIR.