Nonlinear behavior of capacitive micro-beams based on strain gradient theory.

This paper studies the size dependent behavior of materials in MEMS structures. This behavior becomes noticeable for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter and is insignificant for the high ratio of the characteristic size to the length-scale parameter, which is the case of the silicon base micro-beams. However, in some types of micro-beams like gold or nickel bases, the size dependent effect cannot be overlooked. In such cases, ignoring this behavior in modeling will lead to incorrect results. Some previous researchers have applied classic beam theory on their models and imposed a considerable hypothetical value of residual stress to match their theoretical results with the experimental ones. The equilibrium positions or fixed points of the gold and nickel micro-beams are obtained and shown that for a given DC voltage, there is a considerable difference between the obtained fixed points using classic beam theory, modified couple stress theory, and modified strain gradient theory. In addition, it is shown that the calculated static and dynamic pull-in voltages using higher order theories are much closer to the experimental results and are higher several times than those obtained by classic beam theory. [ABSTRACT FROM AUTHOR]