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

In this paper, analysis of free and forced vibration of an FG doubly clamped micro-beam is studied based on the third order shear deformation and modified couple stress theories. The size dependent dynamic equilibrium equations along with boundary conditions are derived using the variational approach. It is assumed that all properties of the FG micro-beam follow the power law form through its thickness. The motion equations are solved employing Fourier series in conjunction with Galerkin method. Also, effects of aspect ratio, power index and dimensionless length scale parameter on the natural frequencies and frequency response 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 indicate that if the thickness of the beam is in the order of the material length scale parameter, size effects are more significant.