Marc Cierzan

Date of Award

January 2012

Document Type


Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Marcellin Zahui


This work shows that a mix of Finite Element Analysis (FEA) and numerical differentiation and integration methods can be used in order to calculate the output charge of a thin piezoelectric film bonded to a shell structure. The method is applied to cases of a cylindrical shell structure, as well as a beam and plate for both generic and shaped piezoelectric films. An overview of the fundamentals of shell vibration theory is presented where the development of the piezoelectric film equation is reviewed and applied to the three different structure cases. The FEA process used is discussed in terms of mode frequency, harmonic, and spectrum analysis. The structural analysis data of the shell substrate is imported into Matlab for further processing using numerical differentiation and integration. The processed data is then used to calculate the film output charge assuming that the piezoelectric film is perfectly coupled with the structure continuum, but does not change its dynamic characteristics i.e. natural frequencies and mode shapes. The results presented herein indicate that the film correctly captures the modes of the structure. However, further investigation is needed for the film output to better predict other structural dynamic properties such as displacement, velocity, or acceleration. The proposed method can be applied to calculate the output charge of films attached to complex structures or structures with complex boundary conditions. Another application is cases where close form equations cannot be derived and the only data available are discrete or experimental. Moreover, in sensor design applications where the film is often shaped so that its output charge corresponds to a specific structural dynamic property, the proposed method greatly simplifies the design process.