Large Amplitude Free Vibration Analysis of Axially Functionally Graded Tapered Rotating Beam by Energy Method

Geometrically nonlinear free vibration behaviour of axially functionally graded non-uniform rotating beams are investigated following variational form of energy method. Nonlinear strain displacement relations are employed to account for geometric nonlinearity present in the system. The static solution of the displacement field of the beam under centrifugal loading is obtained first and then the dynamic problem is formulated as an Eigenvalue problem based on the known static solution. The displacement fields are approximated by linear combination of orthogonally admissible functions and undetermined parameters. The method is validated successfully and results are presented in non-dimensional plane.