In recent years, there has been a surge of interest in using piezoelectric patches attaches to optical surfaces in hope of attaining high precision of optical mirrors with minimal additional weight. Based on results from preliminary investigations, the configuration of thin piezoelectric strip actuators placed in the radial and circumferential line directions of a circular plate (host structure of the mirror) is chosen to control the surface error of the mirror. The major challenges here is the two dimensional actuation effect of the actuator patches, which could induce high order modal deformations and increase the difficulty of surface error control. The purpose of this research is to investigate such effects and propose solutions. A simple model is first developed through Hamilton's principle and discretized using Galerkin's method, thus giving a set of differential equations describing the coupled mechanical and electrical systems. Form the equations, the coupling between the electrical and structural systems for each mode shape can be calculated, thus giving a means to maximize the coupling between the actuator and the mode shapes of interest by changing the actuator's properties. Likewise, the properties can be tailored such that excitation of the unwanted modes can be avoided or reduced. A more comprehensive finite element model is also derived to validate the observations obtained from the simple model. From the analysis, it si found that decoupling of the circumferential action from the radial action of the piezoelectric patches can dramatically improve the performance of the controller, thus achieving a greater reduction in the surface error. Methods to decouple the circumferential strain from the radial strain are then proposed.

Date Published: 16 August 2001
PDF: 11 pages
Proc. SPIE 4327, Smart Structures and Materials 2001: Smart Structures and Integrated Systems, (16 August 2001); doi: 10.1117/12.436578

Published in SPIE Proceedings Vol. 4327:
Smart Structures and Materials 2001: Smart Structures and Integrated Systems
L. Porter Davis, Editor(s)