The use of conventional finite element method for the determination of
flexural vibrations and rotordynamic response of rotating tapered composite shafts
requires a fine mesh of Lagrangian as well as Hermitian finite elements. Such a fine mesh
leads to discontinuities in the shear force and bending moments across the interfaces of
the elements. In addition, the strains in individual plies are discontinuous across the
element interfaces. As a consequence, the natural frequencies, critical speeds and other
dynamic response variables could not be calculated with the required accuracy and
efficiency. The Hierarchical finite element method combines the features and advantages
of the conventional finite element method and the Rayleigh-Ritz method. It can be used
in such a way that the above-mentioned limitations associated with the use of
conventional finite element method can be eliminated. In the present chapter, an efficient
hierarchical finite element formulation is developed for the vibration and rotordynamic
analysis of tapered composite driveshafts. The accuracy and efficiency of this
formulation are demonstrated. Using the developed formulation, the rotordynamic
response including the natural frequencies and critical speeds of tapered composite shafts
are determined. A design parametric study is also presented.
Keywords: Composite shaft, Critical speeds, Driveshaft, Free vibration, Natural
frequencies, Rotordynamics, Taper angle, Tapered shaft.
