Size-dependent vibration analysis of three-dimensional cylindrical microbeams based on modified couple stress theory: A unified treatment

The aim of the study described in this paper is to investigate the size-dependent vibrations of three-dimensional (3-D) cylindrical microbeams by employing the modified couple stress theory with one single material length scale parameter included. The differential equations governing the axial, flexural and torsion vibrations of the microbeams are utilized to formulate the dynamic stiffness matrix. With this formulation the 3-D complex straight and curved beam system can be expressed clearly by means of straight beam elements using the dynamic stiffness method and transfer matrix technique. Since the dynamic properties of beam elements are derived exactly from the governing equation, the results obtained are exact within the range of validity of the assumed governing equations. Our results show that the size effect on vibration properties is significant when the characteristic size of the microbeam is comparable to the internal material length scale parameter. This study provides a useful treatment for predicting the dynamic properties of 3-D cylindrical microbeams and gives insight into the key role played by the internal material length scale parameter.