Influence of damping and fluid loading on the plate vibration control

The aim of this paper is to present the effect of
acknowledging viscous damping, structural internal damping and fluid loading on
active vibration control of a circular plate in case of axially symmetrical
vibrations. It was assumed that a planar vibrating structure located in a finite
baffle and interacting with fluid is driven by a periodic force with constant
amplitude, so the structure radiates the acoustic waves into a surrounding fluid
and the axially-symmetrically located circular piezoelectric actuators are used
to reduce its vibrations. For the purpose of control strategy designing process
the continuous model derived from physical principles for the system under
consideration has been developed. Next, the linear state model was obtained by
reduction and approximation of the continuous model using the orthogonal series
method. After that, the acquired model was used to produce body plots and to
solve corresponding Riccati equation. Obtained control forces led to significant
reduction of the plate vibration and attenuation of accompanied acoustic waves.
The simulations of the active cancellation of the plate vibrations were made
with a Simulink/Matlab computer program.