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 IMMER-SED 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. 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 ENHAN-CED EQUATIONS HAVE BEEN DISCRETIZED OVER THE BEAM AND FLUID DO-MAIN 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 SHOWED THAT MICROPOLAR PARAMETERS OF FLUID DUE TO HAVING DAMPING AND INERTIAL EFFECTS, CHANGES RESONANCE FREQUENCY AND RESONANCE AMPLI-TUDE OF THE SHAFT.