Deterministic and stochastic response of nonlinear coupled bending-torsion modes in a cantilever beam (Q1265311)

We examine the difference between deterministic and random response characteristics of an inextensible cantilever beam (with a tip mass) in the neighborhood of the parametric resonance. The excitation is applied in the plane of largest rigidity, such that the bending and torsion modes are coupled through the excitation. For sinusoidal parametric excitation, the beam experiences instability in the neighborhood of the combined parametric resonance, i.e. when the excitation frequency is in the neighborhood of the sum of the first bending and torsion natural frequencies. The dependence of the response amplitude on the excitation level exhibits three distinct regions: nearly linear behavior, jump phenomena, and energy transfer. The response statistics are estimated using Monte Carlo simulation, and measured experimentally.