Date of Award

Winter 1998

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Aerospace Engineering

Committee Director

Thomas E. Alberts

Committee Member

Chuh Mei

Committee Member

Jeng-Jong Ro

Committee Member

Jen-Kuang Huang


An equation is derived to model the piezoelectric actuators incorporation with flexible structures. This equation permits the comparison of the performance indices over the entire structure for a piezoelectric actuator with constant area, which is unachievable if the Finite Element Method is used for complicated structures.

An index has been developed for placement of piezoelectric actuator for control of vibration of a flexible structure. This index is derived from the definition of H2norm. Computation of the proposed index requires only the natural frequencies and corresponding mode shapes of the structures of interest. The method is well suited to large structure application because of the simplicity of the calculation. The proposed index is valid either for point sensor and actuator or for distributed types such as piezoelectric. Application of the method for different combinations of sensors and actuators has been discussed. Both piezoelectric patch and piezoelectric fiber actuators are used to verify the effectiveness of the proposed index.

The comparison of H2 and H ∞ norms shows good agreement for beam and plate models with single, three, and six modes. The comparison of H2 and H∞ norms is also made for a cantilevered beam with fixed sensor location, and a simply supported plate with a piezoelectric fiber actuator. Agreement between those two norms as well as the proposed index is demonstrated through all the cases.

Imbedded piezoelectric fiber actuators, which, are able to supply anisotropic control actuation, have an optimal fiber orientation, which is related to different structures, but independent of the volume fraction of the PZT fibers. Piezoelectric fiber actuator with volume fraction νf < 1 creates twisting moment, which has better performance than that of a monolithic piezoelectric patch actuator in control of twisting mode.