Stability via nonlocal continuum mechanics

The problem is concerned with the parametric oscillations of a beam subjected to a longitudinal deterministic or stochastic force. The equation, describing the motion of the Euler-Bernoulli beam, is based on the nonlocal elasticity theory and nonlocal damping. The dynamic stability problem is solved for the beam, made from micro- and nano-materials. Asymptotic stability and almost sure asymptotic stability criteria involving a damping coefficient, structure and loading parameters are derived using the method of the maximal Liapunov exponent. (c) 2012 Elsevier Ltd. All rights reserved.