Title page for ETD etd-02212001-145056

Type of Document Dissertation
Author Ashour, Osama Naim
Author's Email Address oashour@vt.edu
URN etd-02212001-145056
Title Nonlinear Control of Plate Vibrations
Degree PhD
Department Engineering Mechanics
Advisory Committee
Advisor Name Title
Nayfeh, Ali H. Committee Chair
Adjerid, Slimane Committee Member
Ahmadian, Mehdi Committee Member
Hajj, Muhammad R. Committee Member
Mook, Dean T. Committee Member
  • Active Control
  • Piezoelectric Ceramics
  • Terfenol-D
  • Smart Materials
  • Saturation
  • Vibration Absorber
Date of Defense 2001-01-17
Availability unrestricted
A nonlinear active vibration absorber to control the vibrations of plates is investigated. The absorber is based on the saturation phenomenon associated with dynamical systems with quadratic nonlinearities and a two-to-one internal resonance. The technique is implemented by coupling a second-order controller with the plate's response through a sensor and an actuator. Energy is exchanged between the primary structure and the controller and, near resonance, the plate's response saturates to a small value.

Numerical as well as experimental results are presented for a cantilever rectangular plate. For numerical studies, finite-element methods as well as modal analysis are implemented. The commercially available software ABAQUS is used in the finite-element analysis together with a user-provided subroutine to model the controller. For the experimental studies, the plate is excited using a dynamic shaker. Strain gages are used as sensors, while piezoelectric ceramic patches are used as actuators. The control technique is implemented using a dSPACE digital signal processing board and a modeling software (SIMULINK). Both numerical and experimental results show that the control strategy is very efficient.

A numerical study is conducted to optimize the location of the actuators on the structure to maximize its controllability. In this regard, the control gain is maximized for the PZT actuators. Furthermore, a more general method is introduced that is based on a global measure of controllability for linear systems.

Finally, the control strategy is made adaptive by incorporating an efficient frequency-measurement technique. This is validated by successfully testing the control strategy for a non-conventional problem, where nonlinear effects hinder the application of the non-adaptive controller.

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