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 that is stiffened in circumferential direction, has been investigated based on the modified couple stress and first order shear deformation theories. modified couple stress theory (mcst) has been used to catch size effects in micro scales. by using first order shear deformation theory and hamilton principle, general equations of motion and corresponding boundary conditions have been derived. free vibration of the structure has been 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 classical continuum theory. results show that effects of the size are considerable and also using stiffeners lead to increase in natural frequencies which is because of increase in stiffness of the cylinder.