Type of Document Dissertation Author Agnes, Gregory Stephen Author's Email Address agnesg@vt.edu URN etd-8897-113619 Title Performance of Nonlinear Mechanical, Resonant-Shunted Piezoelectric, and Electronic Vibration Absorbers for Multi-Degree-of-Freedom Structures Degree PhD Department Engineering Mechanics Advisory Committee
Advisor Name Title Hendricks, Scott L. Kriz, Ronald D. Nayfeh, Ali H. Plaut, Raymond H. Inman, Daniel J. Committee Chair Keywords
- Vibration Absorbers
- Nonlinear Dynamics
- Smart Structures
Date of Defense 1997-09-03 Availability unrestricted Abstract Linear vibration absorbers are a valuable tool used to suppress vibrations due toharmonic 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 Nonlinear 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.
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