Abstract:

A three-dimensional (3D) thermomechanical vibration model is developed for rotating pre-twisted functionally graded (FG) microbeams according to the refined shear deformation theory (RSDT) and the modified couple stress theory (MCST). The material properties are assumed to follow a power-law distribution along the chordwise direction. The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones. The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions (BCs). Several examples are presented to verify the effectiveness of the developed model. By coupling the slenderness ratio, gradient index, rotation speed, and size effect with the pre-twisted angle, the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated. It is found that with the increase in the pre-twisted angle, the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase, while the critical material length scale parameter (MLSP) and rotation speed decrease. The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index, and decreases with the other increasing parameters. Moreover, the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect. Finally, the mode transition is quantitatively demonstrated by a modal assurance criterion (MAC).

Key words: thermomechanical vibration, rotating pre-twisted functionally graded (FG) microbeam, refined shear deformation theory (RSDT), modified couple stress theory (MCST), modal assurance criterion (MAC)