Integral Equation Approach for Beams with Multi-Patch Piezo Sensors and Actuators

An integral equation approach is developed for the solution of an adaptive beam problem with the beam undergoing free vibrations. The beam is controlled by a closed-loop system consisting of multiple patches of sensors and actuators which are bonded to the bottom and top surfaces of the beam. The coupling between sensors and actuators can be chosen arbitrarily and the control is exercised by displacement feedback. The integral equation governing the vibrations of the beam/piezo-patch system is derived by converting the corresponding differential equation, which is non-standard as a result of the discontinuities caused by the piezo patches. The mathematical formulation involves Heaviside and distribution functions in a differential setting, while the integral equation avoids these difficulties and is expressed in terms of a smooth kernel which is developed using a Green's function approach based on suitable patch functions. The numerical results are obtained for various locations of patches, gain factors and coupling configurations, and the first three eigenfrequencies and eigenfunctions of the beam/piezo system are given in table and graph forms.

[1]  László P. Kollár,et al.  Shape Control of Composite Plates and Shells with Embedded Actuators. II. Desired Shape Specified , 1994 .

[2]  Paolo Gaudenzi,et al.  Control of beam vibrations by means of piezoelectric devices: theory and experiments , 2000 .

[3]  Quan Wang,et al.  Optimal placement and size of piezoelectric patches on beams from the controllability perspective , 2000 .

[4]  Osama J. Aldraihem,et al.  Deflection analysis of beams with extension and shear piezoelectric patches using discontinuity functions , 2001 .

[5]  V. Varadan,et al.  Closed loop finite element modeling of active structural damping in the frequency domain , 1997 .

[6]  C. Fuller,et al.  Experiments on active control of structurally radiated sound using multiple piezoceramic actuators , 1990 .

[7]  R. Barboni,et al.  Optimal placement of PZT actuators for the control of beam dynamics , 2000 .

[8]  Vijay K. Varadan,et al.  Natural frequencies of a smart plate with segmented piezoelectric patches , 2000, Smart Structures.

[9]  V. Varadan,et al.  Finite-element modeling of the transient response of MEMS sensors , 1997 .

[10]  Harvey Thomas Banks,et al.  The modeling of piezoceramic patch interactions with shells, plates, and beams , 1995 .

[11]  Ayech Benjeddou,et al.  Advances in piezoelectric finite element modeling of adaptive structural elements: a survey , 2000 .

[12]  Nagi G. Naganathan,et al.  A finite-element static analysis of smart turbine blades , 1997 .

[13]  P. C. Dumir,et al.  Segmented Sensors and Actuators for Thick Plates and Shells Part i: Analysis Using Fsdt , 1999 .

[14]  Liviu Librescu,et al.  Oscillation control of cantilevers via smart materials technology and optimal feedback control: actuator location and power consumption issues , 1998 .

[15]  In Lee,et al.  Optimal placement of piezoelectric sensors and actuators for vibration control of a composite plate using genetic algorithms , 1999 .

[16]  Enrico Fantini,et al.  Genetic Algorithm Optimization for the Active Control of a Beam by Means of PZT Actuators , 1998 .

[17]  Sarp Adali,et al.  Analytical solution technique for multiple-patch piezoelectric sensor-actuator vibration control problems , 2000, Smart Structures.

[18]  Chien-Chang Lin,et al.  Vibration and sound radiation controls of beams using layered modal sensors and actuators , 1998 .

[19]  Huang-Nan Huang,et al.  Vibration control of beam–plates with bonded piezoelectric sensors and actuators , 1999 .

[20]  Vijay K. Varadan,et al.  A review and critique of theories for piezoelectric laminates , 1999 .

[21]  J. C. Bruch,et al.  Optimal piezo-actuator locations/lengths and applied voltage for shape control of beams , 2000 .

[22]  W. H. Huang,et al.  IS A COLLOCATED PIEZOELECTRIC SENSOR/ACTUATOR PAIR FEASIBLE FOR AN INTELLIGENT BEAM? , 1998 .

[23]  J. C. Bruch,et al.  Piezoelectric patch control using an integral equation approach , 2001 .

[24]  Romesh C. Batra,et al.  Analysis of piezoelectric bimorphs and plates with segmented actuators , 2001 .