Vibration control of cantilevered Mindlin-type plates

The cantilevered structure in aerospace engineering is modeled as plates. Based on the Mindlinʹs theory of thick plates, the wave/mode control approach is presented to research the active vibration control of the cantilever plate. In the proposed control approach, the independent modal space control and the wave control are designed and applied to suppress vibration. The vibrational behavior of plate systems can be expressed in terms of waves of both propagating and near-field types. A propagating wave incident upon the line discontinuities gives rise to reflected and transmitted waves of both kinds whose amplitudes may be found from the reflection and transmission coefficients. Since the generalized displacement is continuous, considering the equilibrium of the locations of the wave controllers, the wave reflection and transmission coefficients are calculated. The wave controller is designed, and is intended to absorb the vibration energy, especially at higher frequencies. So the flexural vibration of the plate is suppressed. Vibrations of the Mindlin plate per unit disturbance are investigated. The particular controllers considered are the optimal PD/FIR feedback wave controller and modal controller designed using the optimal control approach. At last, numerical results are analyzed and discussed.