Solutions for the transverse vibration of flexible helicopter blades with elastic boundary conditions using Adomian modified decomposition

In the analyses of rotating helicopter blades, the rotors are usually modelled using classical boundary conditions. However, from the viewpoint of practical engineering this can be considered as a limitation, or an assumption, with elastic boundary supports being widely used in practice. With this in mind an Adomian Modified Decomposition Method (AMDM) is developed here to model the displacement characteristics of a uniform rotating helicopter blade with an offset hub, and with elastic boundary constraints. Centrifugal stiffening is included in the modelling and the AMDM provides accurate solutions with a unified and systematic procedure, while remaining a relatively simple and straightforward calculation method compared to other modal analyses. The elastic restraints are effected using two types of springs, namely translational and rotational. Calculated examples are presented in this work to validate the correctness and effectiveness of the developed method. The influence of the restraining stiffness and rotation speed on the modal characteristics of the rotating beam are investigated and discussed.