Performance of Nonlinear Mechanical, Resonant-Shunted Piezoelectric, and Electronic Vibration Absorbers for Multi-Degree-of-Freedom Structures

Linear vibration absorbers are a valuable tool used to suppress vibrations due to harmonic excitation in structural systems. Limited evaluation of the performance of nonlinear vibration absorbers for nonlinear structures exists in the current literature. The state of the art is extended in this work to vibration absorbers in their three major physical implementations: the mechanical vibration absorber, the inductive-resistive shunted piezoelectric vibration absorber, and the electronic vibration absorber (also denoted a positive position feedback controller). A single, consistent, physically similar model capable of examining the response of all three devices is developed. The performance of vibration absorbers attached to single-degree-of-freedom structures is next examined for performance, robustness, and stability. Perturbation techniques and numerical analysis combine to yield insight into the tuning of nonlinear vibration absorbers for both linear and nonlinear structures. The results both clarify and validate the existing literature on mechanical vibration absorbers. Several new results, including an analytical expression for the suppression region's location and bandwidth and requirements for its robust performance, are derived. Nonlinear multiple-degree-of-freedom structures are next evaluated. The theory of Non-linear Normal Modes is extended to include consideration of modal damping, excitation, and small linear coupling, allowing estimation of vibration absorber performance. The dynamics of the N+1-degree-of-freedom system reduce to those of a two-degree-of-freedom system on a four-dimensional nonlinear modal manifold, thereby simplifying the analysis. Quantitative agreement is shown to require a higher order model which is recommended for future investigation. Finally, experimental investigation on both single and multi-degree-of-freedom systems is performed since few experiments on this topic are reported in the literature. The experimental results qualitatively verify the analytical models derived in this work. The dissertation concludes with a discussion of future work which remains to allow nonlinear vibration absorbers, in all three physical implementations, to enter the engineer's toolbox. Dedication I dedicate this dissertation to my wife, Susan, and daughter, Courtney, whose love and support made it possible. i Acknowledgements I wish to first and foremost acknowledge my wife, Susan. Its the second graduate degree we've struggled through together and although as we've laughed aplenty and cried a little these last three years I couldn't have finished without your love and support. Thank you. My daughter, Courtney, was all of 8 weeks old when we moved to Blacksburg three years ago. I thank her for her understanding when Daddy had to work and for the joy she brought me when I needed …