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.