Publications

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The shape control of thin, flexible structures has been studied primarily for edge-supported thin-plates. For applications such as electromagnetic wave reflectors, corner-supported configurations may prove more applicable since they allow for greater flexibility and larger achievable deflections when compared to edge-supported geometries under similar actuation conditions. Models of such structures provide insight for effective, realizable designs, enable design optimization, and provide a means of active shape control. Models for small deformations of corner-supported, thin laminates actuated by integrated piezoelectric actuators have been developed. However, membrane deflections expected for nominal actuation exceed those stipulated by linear, small deflection theories. In addition, large deflection models have been developed for membranes; however these models are not formulated for shape control. This paper extends a previously-developed linear model for a corner-supported thin, rectangular laminate to a more general large deflection model for a clamped-corner laminate composed of moment actuators and an array of actuating electrodes. First, a nonlinear model determining the deflected shape of a laminate given a distribution of actuation voltages is derived. Second, a technique is employed to formulate the model as a map between input voltage and deflection alone, making it suitable for shape control. Finally, comparisons of simulated deflections with measured deflections of a fabricated active laminate are investigated.

As engineering challenges grow in the ever shrinking world of nano-design, methods of making dynamic measurements of these materials and systems will become important. Electron microscopes have imaged these extremely small samples for years, but are incapable of measuring dynamic events. A means of measuring these nano-scale dynamic events is envisioned by converting an electron microscope into a Doppler velocimeter. This idea proceeds from the analogous concept of laser Doppler velocimetry. However, the obvious solution of using a laser to probe at the nano-scale is not feasible because the diffraction limit of light is orders of magnitude larger than the samples of interest. This paper investigates the theoretical underpinnings of using electron beams for Doppler measurements. Potential issues and their solutions, including electron beam coherence and interference will be presented. If answers to these problems can be found, the invention of the Doppler electron velocimeter could yield a completely new measurement concept at atomistic scales.

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As engineering challenges grow in the ever-shrinking world of nano-design, methods of making dynamic measurements of nano-materials and systems become more important. The Doppler electron velocimeter (DEV) is a new measurement concept motivated by the increasing importance of nano-dynamics. Nano-dynamics is defined in this context as any phenomenon that causes a dynamically changing phase in an electron beam, and includes traditional mechanical motion, as well as additional phenomena including changing magnetic and electric fields. The DEV is only a theoretical device at this point. Lastly, this article highlights the importance of pursuing nano-dynamics and presents a case that the electron microscope and its associated optics are a viable test bed to develop this new measurement tool.

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Measurement of dynamic events at the nano-scale is currently impossible. This paper presents the theoretical underpinnings of a method for making these measurements using electron microscopes. Building on the work of Moellenstedt and Lichte who demonstrated Doppler shifting of an electron beam with a moving electron mirror, further work is proposed to perfect and utilize this concept in dynamic measurements. Specifically, using the concept of ''fringe-counting'' with the current principles of transmission electron holography, an extension of these methods to dynamic measurements is proposed. A presentation of the theory of Doppler electron wave shifting is given, starting from the development of the de Broglie wave, up through the equations describing interference effects and Doppler shifting in electron waves. A mathematical demonstration that Doppler shifting is identical to the conceptually easier to understand idea of counting moving fringes is given by analogy to optical interferometry. Finally, potential developmental experiments and uses of a Doppler electron microscope are discussed.

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