Transverse Free Vibration of Rotating Non-uniform Euler-Bernoulli Beams Using the Adomian Modified Decomposition Method

摘要

The dynamic behavior of rotating beams, including rotor blades, spinning spacestructures and gas turbines is of great practical interest. A recent computation approachcalled the Adomian modified decomposition method (AMDM) is used to carry out thefree transverse vibration analysis of rotating non-uniform Euler-Bernoulli beams usingseveral boundary conditions, rotating speeds and beam lengths. The AMDM allows thegoverning differential equation to become a recursive algebraic equation and theboundary conditions become simple algebraic frequency equations suitable for symboliccomputation. With additional simple mathematical operations on the model, the naturalfrequencies and corresponding closed-form series solution of the mode shape can beobtained simultaneously. For verification of the AMDM method, numerical examples areanalyzed with boundary conditions imposed, including clamped-free, with attention givento convergence of the solutions. As the AMDM technique is systematic, it is foundstraight-forward to modify boundary conditions from one case to the next. Comparisonof results is given with published data and it is found that the current results are in closeagreement with those in the literature.