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Scale Effects of Microcantilever Due to the Nonlocal Long-Range Interactions

Nonlocal variational formulation is established for continuum with the internal long-range interactions. Applying this theory, we develop a new microbeam model, which is used to investigate the scale effects of a micro-cantilever in micro-electro-mechanical system (MEMS). The calculations show that when the thickness of a micro-cantilever is on the micron-order of magnitude, the static deflection of the micro-cantilever increases with the thickness decreasing, but the eigenfrequency remains almost constant. The prediction for the static deflection agrees well with the existing experimental data. This new model provides a concise interpretation, distinguished from the strain gradient theory and surface elasticity, for the scale effects in MEMS. In this model, the scale effects are regarded due to the long-range interactions within material.