Paper Title
Free Vibration Analysis of Axially Functionally Graded Tapered Micro Beam, Using Modified Strain Gradient Elasticity

In this paper, free Vibration analysis of axially functionally graded tapered micro beam are investigated in conjunction with strain gradient elasticity theory. It is assumed that cross section and material properties of the non-uniform and non-homogenous micro beam vary continuously in the longitudinal direction. Natural frequencies of the fixed-free micro beam are obtained by means of Rayleigh-Ritz method. The results show the effects of material properties and taper ratios on natural frequencies of axially functionally graded tapered micro beams and illustrate the effects of considering length scales parameters by comparing the results with those determined by classical theories. To validate and demonstrate accuracy of the present analysis, some results are compared with the available results from the existing literature. Keywords- Vibration, Functionally Graded, Tapered Micro Beam, Strain Gradient Theory.