Modeling of small-scale structures and the extension to the analysis of micro tool's dynamics

Abstract

Small-scale structures are essential elements in today's search for portable and space-constrained miniaturized systems. From micro-turbines, to micro tools and nanocomposites, the idea that "small is the new big thing" is revolutionizing the ways the products of the future are being conceived, designed and built. Due to the extensive applications of miniature systems, the bafflingly complex behavior of their skeletal components, mostly made of micro-and nano-sized beams, plates or shells have to be fully understood. This thesis, therefore, examines the modeling of some small-scale structures based on two recently advanced higher-order theoretical frameworks, namely: Eringen's nonlocal elasticity theory and the modified couple stress theory. Based on these theoretical frameworks, novel higher-order mathematical models of non-uniformly tapered small-scale structures, small-scale structures with pre-twisted deformation and spinning small-scale structures are developed. A new method of analysis, based on the spectral element method, is implemented for parametric analyses of the models. Analyses results revealed that the rate of twist bifurcates the spectrum curve, while the small-scale coefficient improves the dispersion of the traveling wave and generates a group velocity that is more than twice the phase speed for all values of the wavenumbers determined. Under a practical range of the small-scale coefficient, the critical speeds of a spinning, small-scale structure is observed to be at least 20% higher than that predicted by the classical model. The extension of the model to the simulation of the response of a micro end mill revealed that an oversimplification of the model of the micro end mill, in which the micro flute is represented by a model that neglects its rate of twist and length scale, results in a wider margin of difference between the experimental and predicted features.