Vibration Analysis of Thick Functionally Graded Micro-plates Using HOSNDPT and Modified Couple Stress Theory

This paper develops a micro-scale vibration analysis of micro-plates using higher-order shear and normal deformable plate theory in conjunction with modified couple stress theory. The present model includes one material length scale parameter which takes into account the size effects. The equations of motions and boundary conditions are derived using Hamilton's principle. Analytical solutions for the free vibration problem of simply supported rectangular micro-plates are obtained. Numerical results are presented to illustrate the effect of small scale on the dynamic response of functionally graded micro-plates. The results show that the size-dependent effect increases the stiffness of the micro-plate and consequently increases the natural frequencies.