Vibration Analysis of Axially Functionally Graded Timoshenko Beams with Non-uniform Cross-section

The present paper investigates the transverse vibration of a non-uniform axially functionally graded Timoshenko beam with cross-sectional and material properties varying in length direction. Chebyshev collocation method is used to spatially discretize governing partial differential equations motion into time-dependent ordinary terms differentiation matrices. An algebraic eigenvalue equation matrix form then formed study free behavior beams. Several results natural frequencies beams are evaluated compared those published literature assure accuracy proposed model. effects taper ratio, index, slenderness compositions restraint types on tapered examined.