Dynamics of Slender, Flexible Structures

Abstract

Dynamics of slender beam-like structures subjected to rotational motions is studied experimentally, numerically, and analytically within this dissertation. As the aspect ratio of beam-like structures is increased (i.e., as the structures become slender), the structure can undergo large elastic deformations, and in addition, the torsional and lateral motions can be strongly coupled. Two different paradigms of rotor systems are constructed and used to investigate coupled torsional-lateral motions in slender rotating structures. The first rotor model is a modified version of the classical Jeffcott rotor, which accounts for torsional vibrations and stator contact. Analysis and simulations indicate that torsional vibrations are unlikely to exist during forward synchronous whirling, and reveal the presence of phenomena with high-frequency content, such as centrifugal stiffening and smoothening, during backward whirling. The second rotor model is a nonlinear distributed-parameter system that has been derived with the intent of capturing dynamics observed in an experimental apparatus with slender, rotating structures. Nonlinear oscillations observed in the experiments contain response components at frequencies other than the drive speed, a feature that is also captured by predictions obtained from the distributed-parameter model. Further analysis of the governing partial-differential equations yields insights into the origins (e.g., nonlinear gyroscopic coupling and frictional forces) of the nonlinear response components observed in the spectrum of the torsion response. Slender structures are often subject to large deformations with pre-stress and curvature, which can drastically alter the natural frequencies and mode shapes when in operation. Here, a geometrically exact beam formulation based on the Cosserat theory of rods is outlined in order to predict the static configuration, natural frequencies, and mode shapes of slender structures with large pre-stress and curvature. The modeling and analysis are validated with experiments as well as comparisons with a nonlinear finite element formulation. The predictions for the first eight natural frequencies are found to be in excellent agreement with the corresponding experimentally determined values. The findings of this dissertation work have a broad range of applications across different length scales, including drill strings, space tethers, deployable structures, cable supported structures (e.g., bridges and mooring cables), DNA strands, and sutures for non-invasive surgery to name a few.