Vibrations of circular plate interacting with an ideal compressible fluid

In this work, numerical simulations describing the circular plate vibration suppression are presented. It was assumed that the vibrating plate is clamped at the circumference of a planar finite baffle and that it interacts with an ideal homogeneous compressible fluid. The formal solution of the fluid-plate-coupled equation is given for a plate driven by a harmonic surface force with constant density; the state-space realisation of the model is given. Three parameters that characterise fluid loading, internal damping of the plate material and the ratio of the plate radius to the baffle size are included in this model. The modern control theory is then applied to the system state-space equation. An optimal reduction of the plate vibrations was obtained for the point control force located centrally using a linear quadratic regulator (LQR). The simulations of the active attenuation of the plate vibrations were made with a Simulink/Matlab® computer program. The results indicate that it is possible to achieve a significant reduction of the vibration amplitude using only one control force.