A two-scale model for one-dimensional arrays of cantilevers and its verification |
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| Authors: | Hui Hui Michel Lenczner Emmanuel Pillet Scott Cogan |
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| Institution: | 1. Department of Chemistry, University College London, Christopher Ingold Laboratories, 20 Gordon Street, London WC1H OAJ, United Kingdom;2. UCL Energy Institute, Central House, 14 Upper Woburn Place, London WC1H 0HY, United Kingdom;3. School of Engineering and Materials Science, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom |
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| Abstract: | We present a simplified model of the mechanical behavior of large arrays of cantilevers in the dynamic operating regime. The supporting base is assumed to be elastic thus cross-talk effect between the cantilevers is taken into account. Beforehand, the model has been mathematically justified starting from a thin plate model, using the two-scale approximation theory issued from homogenization theory and taking into account the strong heterogeneities of the system. The resulting model is not standard, so in this paper dedicated to its verification, we focus on some of its features in particular those related to the structure of its eigenmodes by both a qualitative and a quantitative analysis. |
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