Complex Behavior of a Buckled Beam Under Combined Harmonic and Random Loading

Abstract

Nonlinearities have long been avoided in the design of structural systems. This was done to make problems tractable, to fit within current design paradigms, and often with the assumption that the resulting design would be conservative. Computational methods have made the investigation of nonlinear systems possible, which may yield more accurate and optimal designs. However, in venturing into the nonlinear regime, a designer must be aware of potential pitfalls, one of which is the possibility of unsafe responses “hiding in the weeds” of parameter or initial condition space. In this paper, an experimental study on a damped, post-buckled beam in the presence of noise is used to show that co-existing stationary solutions may be present in real-world scenarios. Stochastic resonance, a surprising phenomenon in which a small harmonic load interacts with, and magnifies the response to, an otherwise pure random load, is also studied and observed to occur in the beam.