Extraction of Natural Frequencies and Mode Shapes of Rotating Beams by Variational Iteration Method

Flapwise flexural vibration of rotating beams has been extensively studied since the 1970s. Existing methods for solving the aforementioned vibration problem range from the conventional finite element method to variable-order finite element method, Frobenius method, differential transformation method and dynamic stiffness method (DSM). Although various approximation methods are available, most of these methods are based on perturbation or discretization of the governing equation, often leading to tedious calculations. This paper re-examines flapwise flexural vibration of rotating beams using the method of variational iteration, which is relatively new and capable of providing accurate solutions for eigenvalue problems. The extracted natural frequencies and mode shapes for sample rotating beams with various rotational speeds and hub radii are compared with existing results that were published in the open literature.