Effect of Fluid Mass on Non-Linear Natural Frequencies of a Rotating Beam
The non-linear natural frequencies of the first three modes of a beam clamped to a rigid rotating hub and carrying a distributed fluid along its span are investigated. The mathematical model is derived using the Lagrangian method and the continuous system is discretized using the assumed mode method. The resulted unimodal nonlinear equation of motion was solved using two methods; harmonic balance (HB) and time transformation (TT), to obtain approximate analytical expressions for the nonlinear natural frequencies. Results have shown that the two terms harmonic balance method (2THB) is more accurate than the time TT method. Results for the effect and type of distribution, i.e. uniform or linearly distributed, on the variation of the nonlinear natural frequency with the rotational speed of the system and how they affect the stability are studied and presented in non-dimensional form.