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| Study on Scale Effects for Free-vibrating of Four edges Simply Supported Micro-plate Based on the Cosserat Theory |
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Abstract The mechanical properties of a certain material depend on its internal structure, and study on scale effects of microstructure dynamics is greatly significant. It is well know most of the micro/nano devices are typically plate-structured. The lack of literature on study on the scale effect for micro-plates has significantly limited the designing and application of micro/nano devices. The free vibrating differential equation of four edges simply supported (SSSS) micro-plate is presented using the modified Cosserat theory in this paper. Consequently, we obtain the formula of natural frequencies that meet SSSS boundary conditions and analyze the scale effects for natural frequencies of micro-plates with different dimensions. The results show that scale effects is highly significant on the free vibrating natural frequency when characteristic length and micro-plates thickness are close, and the natural frequencies increase along with the increase of characteristic length. Additionally, the scale effects depend on thickness of micro-plate. The theory we presented is of fundament importance for the application of microstructure system.
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Received: 05 November 2010
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2012, Vol. 33 