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This book addresses the solution of rotating beam free-vibration problems using the finite element method. It provides an introduction to the governing equation of a rotating beam, before outlining the solution procedures using Rayleigh-Ritz, Galerkin and finite element methods. The possibility of improving the convergence of finite element methods through a judicious selection of interpolation functions, which are closer to the problem physics, is also addressed. The book offers a valuable guide for students and researchers working on rotating beam problems - important engineering structures used in helicopter rotors, wind turbines, gas turbines, steam turbines and propellers - and their applications. It can also be used as a textbook for specialized graduate and professional courses on advanced applications of finite element analysis.