Simulation of tapered rotating beams with centrifugal stiffening using the Adomian decomposition method

The Adomian modified decomposition method (AMDM) is employed for the free transverse vibration analysis of rotating non-uniform Euler-Bernoulli beams using several boundary conditions, rotation speeds, and beam lengths. The equation of motion includes the axial force due to centrifugal stiffening. The AMDM allows the governing differential equation to become a recursive algebraic equation and after additional simple mathematical operations on the model, the natural frequencies and corresponding closed-form series solution of the mode shape can be obtained simultaneously. The AMDM technique is systematic, so it is straightforward to modify the boundary conditions for specific cases. Comparisons with previously reported results demonstrated that the results obtained by the proposed method were in close agreement.