Free Vibrations of Spinning Beams Under Nonclassical Boundary Conditions Using Adomian Modified Decomposition Method

This study employs the Adomian modified decomposition method (AMDM) for the dynamic analysis of Euler–Bernoulli beams spinning about their longitudinal axes under various boundary conditions. Based on the AMDM, the governing differential equations for the spinning beam become a recursive algebraic equation system. By using the boundary condition equations, the natural frequencies can be readily obtained. The computed results under different classical and nonclassical boundary conditions as well as spinning speeds are presented. The accuracy is assured from comparison with published results. It is shown that the AMDM offers an accurate and straightforward method of free vibration analysis of spinning beams with arbitrary boundary conditions.