Dynamics of prestressed translating or rotating anisotropic plates subject to transverse loads and heat sources.

Abstract

This dissertation deals with the application of finite element methods for the analysis of translating or rotating plates, based on the Mindlin plate theory and von Karman strain expression, in the context of linear thermoelasticity. Several integration methods were tried and compared in solving for the dynamic deflections of the plate. A second-order accurate implicit method is chosen in this study, because with it one can select a time increment sufficiently large, without numerical stability problems, based on the accuracy needed. For the translating thin plate (applicable to tape drive mechanisms, band saws, etc.) the eigenvalues and the critical speeds, when there are in-plane tensions, are shown to be consistent with published results for several different boundary conditions. Finally, the effects of temperature distribution, microstructures, and anisotropic material properties on the transverse dynamics are studied. The rotating disk has many applications as in floppy, hard, compact, laser, and, recently, optical disk drives, etc. The critical speed of a disk is obtained to validate the formulation and programming. Dynamic responses for this case are obtained as parametrized by the rotating speed. Effects of the temperature distribution and microstructures are also observed in this case. A conclusion of this study is that the effects of temperature are crucial in the analysis of translating or rotating plates, since the variation of temperature can be significant. This is especially true for equipment in which a heat source is used as a means of recording or erasing data and for equipment in which the amount of generated or transferred heat is significant. Homogenization theory, applicable to not only determining the global material properties for composite materials like laminate or fiber reinforced matrix, but also computing microscopic stress levels, was applied to laminate and fiber-reinforced matrix cases to obtain orthotropic material properties. The effect of anisotropy on the deflection of plates is also shown to be significant.