Experimentally validated geometrically exact model for extreme nonlinear motions of cantilevers

Farokhi, Hamed, Xia, Yiwei and Erturk, Alper (2022) Experimentally validated geometrically exact model for extreme nonlinear motions of cantilevers. Nonlinear Dynamics, 107 (1). pp. 457-475. ISSN 0924-090X

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Abstract

A unique feature of flexible cantilevered beams, which is used in a range of applications from energy harvesting to bio-inspired actuation, is their capability to undergo motions of extremely large amplitudes. The well-known third-order nonlinear cantilever model is not capable of capturing such a behaviour, hence requiring the application of geometrically exact models. This study, for the first time, presents a thorough experimental investigation on nonlinear dynamics of a cantilever under base excitation in order to capture extremely large oscillations to validate a geometrically exact model based on the centreline rotation. To this end, a state-of-the-art in vacuo base excitation experimental set-up is utilised to excite the cantilever in the primary resonance region and drive it to extremely large amplitudes, and a high-speed camera is used to capture the motion. A robust image processing code is developed to extract the deformed state of the cantilever at each frame as well as the tip displacements and rotation. For the theoretical part, a geometrically exact model is developed based on the Euler–Bernoulli beam theory and inextensibility condition, while using Kelvin–Voigt material damping. To ensure accurate predictions, the equation of motion is derived for the centreline rotation and all terms are kept geometrically exact throughout the derivation and discretisation procedures. Thorough comparisons are conducted between experimental and theoretical results in the form of frequency response diagrams, time histories, motion snapshots, and motion videos. It is shown that the predictions of the geometrically exact model are in excellent agreement with the experimental results at both relatively large and extremely large oscillation amplitudes.

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