Vibration Analysis of Flexible Rotating Rings Using a Spectral Element Formulation

In this work, the forced response of rotating rings exhibiting nonperiodic and periodic variations in material properties and geometry is assessed by means of the spectral element method (SEM). Based on the Euler–Bernoulli beam theory, a spectral element for a planar rotating ring is derived. This spectral element allows the investigation of the effects of structural damping, internal pressure and elastic foundations in the harmonic response of rotating rings. The dynamic response of rotating rings including periodic imperfections that lead to band gap effects is addressed. The spectral element formulation provides exact solutions within the range of validity of the applied theory using a reduced number of degrees-of-freedom. Thus, it contributes to reducing the computational time. It also provides a straightforward way to solve structural dynamics problems including arbitrary boundary conditions and discontinuities. The proposed formulation is validated by comparison with analytical solutions, which are available only for uniform homogenous rings.