Differential transformation and differential quadrature methods for centrifugally stiffened axially functionally graded tapered beams

• Two methods, DTM and DQEL are applied for free vibration analysis of rotating FG tapered beams.
• Frequencies are obtained by considering material nonlinearity, taper ratio and speed parameter etc.
• These two methods are also as powerful as Finite element and Finite difference methods.
• Both the methods do not need the construction of admissible function to satisfy BCS a priori.
• Frequencies of homogeneous beam are higher than non homogeneous beam except CF and PF BCS.

The free bending vibration of rotating axially functionally graded (FG) Euler–Bernoulli tapered beams (ETB) with different boundary conditions are studied using Differential Transformation method (DTM) and differential quadrature element method of lowest order (DQEL). These two methods are capable of modeling any beam whose cross sectional area and moment of inertia vary along the beam. In order to verify the competency of these two methods, natural frequencies are obtained for problems by considering the effect of material non-homogeneity, taper ratio, rotating speed parameter, hub radius and tip mass. The results are tabulated and compared with the previous published results.