Analysis and control of thermoelastic vibrations in plate structures.

Abstract

This work is concerned with the analysis and control of thermoelastic vibrations in rectangular plate structures using piezoelectric materials for the sensor(s) and actuator(s). Both isotropic and symmetrically laminated, cross-ply composite plates subjected to mechanical and thermal loads are studied. Chapter 2 develops an analytical solution for the case of a simply supported, rectangular symmetrically laminated, cross-ply composite plate subjected to a thermal shock. The analysis includes the interaction between the strain and temperature fields and, in the case of the composite plates, investigates the effect of accounting for the orthotropic material properties in the governing elastic and thermal equations. The resulting solution for the vibration of the composite plate is compared to a previous analysis of a homogeneous, isotropic, rectangular plate. Comparison indicates that, while the solutions have similar forms, the explicit summation in the isotropic solution has been replaced by implied summations resulting from vector inner product multiplications in the composite solution. Chapter 3 develops a new coupled thermoelastic finite element model of a rectangular plate with embedded piezoelectric patches suitable for closed loop vibration control. The open loop response of this model subjected to a thermal shock is validated against the response of the Chapter 2 solution, and the closed loop response is validated against previous work. In both cases, the new finite element model compared favorably. Chapter 4 describes an approach used to design controllers suitable for closed-loop control of plate thermoelastic vibrations, and applies this approach to two different design problems. Chapter 5 presents the conclusions and suggestions for future work.*

*This dissertation includes a CD that is compound (contains both a paper copy and a CD as part of the dissertation). The CD requires the following applications: Microsoft Excel, Compaq Visual FORTRAN 6.0, AMRLAB 6.1, Maple V 5.1, FEModel Development, Scientific Word 3.51, Adobe Illustrator 7.0.