Vibration Analysis of FG Micro-Beam Based on the Third Order Shear Deformation and Modified Couple Stress Theories

In this paper, free vibration analysis and forced vibration analysis of FG doubly clamped micro-beams is studied based on the third order shear deformation and modified couple stress theories. The size dependent dynamic equilibrium equations and both the classical and non-classical boundary conditions are derived using a variational approach. It is assumed that all properties of the FG micro-beam follow a power law form through thickness. The motion equations are solved by employing Furrier series in conjunction with Galerkin method. Also, effects of aspect ratio, power index and dimensionless length scale parameter on the natural frequencies and amplitude-excite frequency curves are investigated. Findings indicate that dimensionless frequencies are strongly dependent on the values of the material length scale parameter and power index. The numerical results of this study indicate that if the thickness of the beam is in the order of the material length scale parameter, size effects are more significant.