On mathematical modelling of linear flexural vibrations of spinning Rayleigh beams

The present paper discusses the linearization schemes effects on the mathematical modelling of 3D bending vibrations of a spinning Rayleigh beam. Indeed, four linearization approaches, that differ according to the stage of introduction of the linearization process in the computations, are discussed. It is shown that the linearization scheme influences the centrifugal and Euler forces terms. Consequently, the use of early linearization schemes in the case of Rayleigh beams should be done with caution especially for high spinning velocities and low slenderness ratios. Moreover, it is shown that the stability zones are also affected by the used scheme. Furthermore, it is proven that the linear equations of 3D flexural vibrations of spinning Euler-Bernoulli beams are independent of the linearization scheme. On the other hand, the present work presents a general mathematical model that encompasses all linear models, obeying the same assumptions, of bending vibrations of spinning Rayleigh beams with nonconstant spinning velocities either expressed in the rotating or in the inertial frames. (C) 2018 Elsevier Ltd. All rights reserved.