The dynamical response analysis of piezoelectric flexible structures based on model reduction

Piezoelectric materials are finding increasing applications in active vibration control of structures. A widely used modeling technique for piezoelectric flexible structures is the assumed modes method which results in an infinite dimensional model of the composite structure. The paper builds the model of piezoelectric flexible structures and calculates the modal frequency by the application of ANSYS software, extracts the required modes according to the method of model reduction based on the spatial H₂ norms of modes. The optimal location of the piezoelectric patches is ascertained by applying the D-optimal design principle, which avoids the locationpsilas randomicity as well as reduces the number of sensors/actuators in terms of not affect the controlling effect. Finally, the paper takes a piezoelectric cantilever beam as an example and gives the step response curve of the system. The results show that this method has more superiority than the ordinary modes truncation.