| Summary: | 碩士 === 國立中興大學 === 機械工程研究所 === 81 === Although many researches had been done on the vibration control
of elastic beams using piezoelectric sensors and actuators , in
most of these works either Bernoulli-Euler or Timoshenko beam
theory is adopted. As a result, the emphasis is on the
suppression of the bending vibration, leaving out the important
issue of the control of the torsional vibration. The main goal
of this thesis is to develop methods of controlling the bending
and torsional vibration of composite beam simultaneously with
piezoelectric sensors and actuators. Toward this end, first, an
improved beam theory incorporating both bending and torsional
deformation effects is employed. Next, the Hamilton principle
and finite element method are used to derive the equations of
sensor and of motion of beams containing driving source from
the piezoelectric actuator. These equations are then
transformed into state-space form convenient for control
design. Linear quadratic Gaussian (LQG) technique is applied to
design the controller for vibration suppression. It is shown
that through the design of the observer or by choosing
appropriate sensor's locations, the performance of the
controller can be improved significantly. As for the control of
the torsional vibration, two schemes are proposed. One approach
is making use of the mechanical deformation coupling effect
existing in the composite materials. Since if there exists a
coupling between the bending and torsional vibration, the
torsional vibration can be suppressed through the control of
the bending vibration. The other approach is to arrange the
piezoelectric material in such a way that its principal
material direction form an angle (often called skew angle) with
beam axis. Then if, furthermore, the dielectric constants d31
and d32 are not equal, the piezoelectric sensors and actuators
are able to sense and control both bending and torsional motion.
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