In the current study, a comprehensive analysis of nonlinear free vibrations of a flexible rotating beam attached with a setting angle to a rigid hub is perused. The system is supposed to be subjected to an external torque and a rotation dissipation load which collectively referred to as perturbations. A set of two strongly coupled second-order ordinary nonlinear differential equations with an ignorable coordinate is used to depict the dynamics of the individual mode in plane flexural deflection of the arm and its overall rotational motion. For the unperturbed system which is our especial case in this work, the system angular momentum parameter, not the hub rotational speed, becomes a specified constant of motion. Furthermore, in order to consider the effect of beam deflections on the overall motion and vice versa, utilizing torque-controlled approach is necessary. It is noteworthy that here three powerful analytical methods for instance Modified Differential Transformation Method (MDTM), Variation Iteration Method (VIM) and finally Homotopy Perturbation Method (HPM) have been introduced to investigate the comportment and frequency of cantilever rotating beams with a setting angle. These methods are useful and practical for solving a wide variety of nonlinear equations. Comparisons amongst the obtained results by all the presented methods and Numerical solution reveal that all the afore-mentioned methods are significantly effective and efficient especially MDTM.
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