Free vibration analysis of functionally graded stiffened micro-cylinder based on the modified couple stress theory

In this paper, free vibration of the micro-cylinder made by functionally graded material stiffened in circumferential direction was investigated based on modified couple stress and first-order shear deformation theories. Modified Couple Stress Theory (MCST) was used to catch size effects in micro scales. By using first-order shear deformation theory and Hamilton's principle, the general equations of motion and corresponding boundary conditions were derived. Free vibration of the structure was investigated by implementing simply-supported boundary condition as a common case. The effects of different parameters, such as dimensionless length scale parameter, distribution of FGM properties, number of stiffeners, thickness and length on the natural frequencies, were calculated and compared with those of classical continuum theory. Results show that effects of the size are considerable; moreover, using stiffeners leads to an increase in natural frequencies due to an increase in stiffness of the cylinder. (C) 2018 Sharif University of Technology. All rights reserved.