Studying Torsional Vibration of a Micro-shaft in a Micro-scale Fluid Media based on Non-classical Theories

Abstract In this paper, torsional vibration of a micro-shaft in interacting with a micro-scale fluid media has been investigated. The presented mathematical model for this study is made up of a micro-shaft with one end fixed and a micro-cylinder at its free end which is immersed in a micro-scale fluid media. The micro-shaft can be actuated torsionally via applying an AC voltage to the capacitive plates around the micro-shaft and the outer fixed cylinder. As fluids and solids behave differently in micro scale than macro, the surrounding fluid field in the gap and also the micro-shaft have been modeled based on non-classical theories. Equation of motion governing angular displacement of the micro- shaft and also equations of motion of the fluid field have been derived based on non-local elasticity and micro-polar theories. The coupled differential equations have been transformed to an enhanced form with homogenous boundary conditions. The enhanced equations have been discretized over the beam and fluid domain using Galerkin method. Effects of non-local parameter of the micro-shaft and also micro-polar parameters of the fluid field on the response of the micro-shaft have been studied. We have shown that micropolar parameters of fluid due to having damping and inertial effects, changes resonance frequency and resonance amplitude of the shaft.