On the stability of a rod under deterministic and stochastic loading with allowance for nonlocal elasticity and nonlocal material damping

The stability of rods, whose material is characterized by nonlocal elasticity and nonlocal damping typical of composite and nanomaterials, has been studied using the example of a rod with hinged ends. This rod is affected by deterministic or random stationary longitudinal force. In the case of deterministic force stability is understood in the Lyapunov sense, while in the stochastic case stability is almost certain. In both cases the maximum Lyapunov exponent is used for investigating stability stability investugation. The effect of nonlocality parameter values on the maximum Lyapunov indexes exponent has been studied under the action of constant, periodic, and random longitudinal forces on the rod. © 2015, Allerton Press, Inc.