Performance of Nonlinear Mechanical, Resonant-Shunted Piezoelectric, and Electronic Vibrations 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.Air Force Inst of Tech Wright-Patterson AFB OH is the author of 'Performance of Nonlinear Mechanical, Resonant-Shunted Piezoelectric, and Electronic Vibrations Absorbers for Multi-Degree-of-Freedom Structures', published 1997 under ISBN 9781423582885 and ISBN 1423582888.