Experimental and Computational Characterization of Nonlinear Vibration Response of "Plunging" Beams

In this study the vibration response of three different slender “plunging” beams of uniform rectangular cross-section is investigated both experimentally and computationally. In the experimental part of the research, beams prepared from a 2-ply unidirectional DA409U/G35 graphite/epoxy laminate, a Rohacell ® IG-35 foam-core sandwich composite with one ply unidirectional graphite/epoxy prepreg facings on each side, and an AISI 1010 cold-rolled steel shim stock are used. The beams are subjected to plunging (flapping) motion from their clamped end by means of a single-degree-of-freedom flapping mechanism. The flapping experiments are performed at a fixed flapping amplitude of ±20° over a range of flapping frequencies between 1 Hz and 10 Hz. Deformation of the beams is characterized through the use of a high-speed camera and foil strain gages. The flapping mechanism is shown to produce reliable kinematics when inertial loading transferred from the beam to the mechanism is not too excessive. Experimental strain and tip deflection data reveal that for the amplitude and frequencies of flapping tested the response is periodic and increases with increasing flapping frequency. At low flapping amplitudes the computational results indicate a possible universal scaling of the normalized (by length) beam tip deflection with an inertial load. In addition at large flapping amplitudes the beam tip deflections are relatively insensitive to a change in flapping amplitude. Examination of the steel beam computational phase plane results indicate a possible transition to non-periodic response at flapping amplitudes of 40° and higher. Further computational and experimental investigation is necessary to determine whether the response is truly aperiodic and if so whether it ultimately results in a chaotic dynamics.