Shannon Entropy in Stochastic Analysis of Some Mems

Abstract

This work is focused on the numerical determination of Shannon probabilistic entropy for MEMS devices exhibiting some uncertainty in their structural response. This entropy is a universal measure of statistical or stochastic disorder in static deformation or dynamic vibrations of engineering systems and is available for both continuous and discrete distributions functions of structural parameters. An interval algorithm using Monte Carlo simulation and polynomial structural response recovery has been implemented to demonstrate an uncertainty propagation of the forced vibrations in some small MEMS devices. A computational example includes stochastic nonlinear vibrations described by the Duffing equation calibrated for some micro-resonators, whose damping is adopted as a Gaussian, uniformly and triangularly distributed input uncertainty source.

Keywords

• Shannon entropy
• MEMS vibrations
• Duffing equation
• random damping