Title page for ETD etd-8897-113619

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
  • Vibration Absorbers
  • Nonlinear Dynamics
  • Smart Structures
Date of Defense 1997-09-03
Availability unrestricted
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 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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