Finite Element Analysis of Vibration Behavior of Micro-Rotors Utilizing a Developed Strain Gradient-Based Beam Element

In this paper, a three-dimensional finite element model is developed based on the strain gradient theory to investigate the vibration characteristics of micro-rotors. The model is not only capable of dealing with small-size effects, but also the flexibility of bearings, internal damping and mass eccentricity in the system. The expressions related to the strain energy of the shaft of the microrotor are derived on the basis of strain gradient theory together with the kinetic energy of the system considering mass eccentricity in the disk and rotary inertia and gyroscopic effects of the rotating shaftdisk system. By using the extended Hamilton’s principle to obtain weak forms of governing equations and approximating displacement components by special interpolation functions which can be used to model a strain gradient based micro-beam, equations of the motion are discretized into a finite element form. The natural frequencies, critical speeds and the threshold of instability rotational speed of the micro-rotor are obtained by transforming discretized equations of motion into state space form. The response of the micro rotor under excitation of the mass eccentricity of the disk in forced vibrations is also presented. Numerical results show profound effects of higher order material constant on vibration characteristics of the micro-rotor.