26 July 2004 Shape optimization of microcantilevers for mass variation detection and AFM applications
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The paper proposes an analytical model-based, lumped-parameter algorithm which enables identifying a microcantilever design that will give the optimized performance with regard to stiffness and resonant frequency values in terms of a corresponding shape and its related geometric parameters. The targeted microcantilever applications are mass variation detection and atomic force microscopy (AFM) whereby the monitored system parameters are the changes in deflection and/or the natural frequency. A design set comprises several configurations, each of them being defined by analytical curves, such as straight lines, circular or elliptical arcs, and which are quantified in terms of compliances/stiffnesses and resonant frequencies by algebraic equations. The model is capable of discerning both the intensity of external excitation and the first resonant frequencies for a given microcantilever. Finite element simulation results of the static and resonant response for these microcantilevers confirm the analytical model predictions. The optimization algorithm, which is based on this model, focuses on maximizing the master bending compliance and on spacing out the first resonant frequency from the subsequent ones in order to increase the response sensitivity of the microcantilever. The model-based optimization algorithm is a relatively low-cost and sufficiently-accurate calculation procedure, which is formulated as an alternative to existing finite element simulation.
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Ephrahim Garcia, Nicolae Lobontiu, Yoonsu Nam, Rob Ilic, Timothy Reissman, "Shape optimization of microcantilevers for mass variation detection and AFM applications", Proc. SPIE 5390, Smart Structures and Materials 2004: Smart Structures and Integrated Systems, (26 July 2004); doi: 10.1117/12.540043; https://doi.org/10.1117/12.540043

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