Abstract:

Based on the scaling function transform of the Daubechies wavelet theory, an explicit expression of identification of deflection for cantilevered beam plates with variable thickness is obtained by the measurable electric charges and electricity from the piezoelectric sensors attached on the structures. After that, a control programme to the control system with piezoelectric sensors and actuators is established by means of a control law of feedback of negative signals of the identified deflection and its velocity to suppress vibrations of the structures. Due to the characteristic that the scaling function transform has a function of low pass filter which can auto filter out those signals of higher order dependent upon the resolution level of the wavelet theory, this control program on the basis of the wavelet theory can avoid the phenomenon of control instability that is caused by the coupling of spilling over of sensing and actuating, or in other words, that some higher order vibrations are excited when a lower order vibration is suppressed. The numerical simulations show that this control program can effectively suppress those disturbances spread from the lower order modals of the structure when the number of order of the disturbance is not greater than the number of piezoelectric actuators or sensors employed.

Key words: beam plates with variable thickness, dynamic control with piezoelectric sensors and actuators, scaling function transform of wavelet theory, identification of deflection, control program, numerical simulations