Linearly coupled shaft-torsional and blade-bending vibrations in multi-stage rotor-blade systems

In an attempt towards the understanding of coupling effects between shaft-torsional and blade-(in plane) bending vibrations in turbomachinery and other rotating bladed structures, an idealized model is considered where the blades are represented by uniform Euler–Bernouilli beams. A synthetical, multi-frame and mixed (consisting in a coalescence of finite element and Galerkin methods) approach is used to derive a linearized mathematical model for the system. It is shown that the related eigenanalysis problem splits into two separate sub-problems corresponding to two kinds of possible normal mode motions. Eigenanalyses are performed concerning single as well as multi-stage rotor-blade system examples. Parametric studies are presented on the variation of the eigenfrequencies with system parameters. Eigenvalue loci veering phenomena are shown to occur, causing departure of the eigenvalues from those obtained through an uncoupled analysis. Mode shape examples are also presented.