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.

[1]  Robert C. Wetherhold,et al.  Optimal Size and Location of Piezoelectric Actuator/Sensors: Practical Considerations , 1997, Adaptive Structures and Material Systems.

[2]  Hemanshu R. Pota,et al.  Multivariable transfer functions for a slewing piezoelectric laminate beam , 1992, [Proceedings 1992] IEEE International Conference on Systems Engineering.

[3]  Wodek Gawronski,et al.  Balanced Control of Flexible Structures , 1995 .

[4]  Hemanshu R. Pota,et al.  Vibration analysis using symbolic computation software , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[5]  Robert L. Clark,et al.  Accounting for Out-of-Bandwidth Modes in the Assumed Modes Approach: Implications on Colocated Output Feedback Control , 1997 .

[6]  Fred Y. Hadaegh,et al.  Optimal experiment design for identification of large space structures , 1988, Autom..

[7]  C. I. Tseng,et al.  Distributed piezoelectric sensor/actuator design for dynamic measurement/control of distributed parameter systems: A piezoelectric finite element approach , 1990 .

[8]  Ian R. Petersen,et al.  Spatial balanced model reduction for flexible structures , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[9]  I.R. Petersen,et al.  Active control of noise and vibration in acoustic ducts and flexible structures-a spatial control approach , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[10]  Hemanshu R. Pota,et al.  Experimental verification of transfer functions for a slewing piezoelectric laminate beam , 1995 .

[11]  Ian R. Petersen,et al.  BROADBAND DISTURBANCE ATTENUATION OVER AN ENTIRE BEAM , 1999 .

[12]  Leonard Meirovitch,et al.  Elements Of Vibration Analysis , 1986 .