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

Abstract

Abstract. 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.

Finite Element Model and Size Dependent Stability Analysis of Boron Nitride and Silicon Carbide Nanowires/Nanotubes

“…Rafaeinejad et al showed clearly the e ects of foundation, gradient index, aspect ratio, and nonlocal parameter on stability and vibration analysis. More recently, Jabbarian and Ahmadian conducted the free vibration analysis of a functionally graded sti ened micro-cylinder [104]. They took the size e ect into consideration using the Modi ed Couple Stress Theory (MCST).…”

Size Effect Investigation on Lateral Vibrations of a Micro Drill Subjected to an Axial Load Using the Modified Couple Stress Theory

“…The classical continuum mechanics theories are unable to explain and predict the mechanical behavior of the materials in small sizes. Therefore, some of the non-classical continuum theories such as strain gradient theory, couple stress theory, nonlocal elasticity theory, and surface elasticity theory have been introduced to capture the size e ect on elastic deformation behavior of micro-structures [14][15][16][17][18][19][20][21][22][23].…”