Natural Frequencies of Rotating Cantilever Plates

TL;DR: In this article, a Galerkin-based methodology is implemented to obtain the modal characteristics of rotating plate structures and the results for the non-dimensional natural frequencies as a function of the nondimensional rotating speed are presented in the form of natural frequency maps.

Abstract: Rotating blades are widely used in turbomachinery applications. In these applications, blades fail frequently because of large amplitude vibrations. These large amplitude vibrations are related to the resonances of the blade structure. Thus, accurate estimation of natural frequencies of such rotating structures is of utmost importance. As documented in the literature, a widely used model of such blade structures consists of rotating beams or plates. The objective of this work is to determine the natural frequencies of rotating plate structures. Starting from the non-dimensional governing equation of the rotating staggered cantilever plate as presented by Sun et al. (J Sound Vib 332(5):1355–1371, 2013) [1], the corresponding weighted residual statement is derived. In the present study, a Galerkin-based methodology is implemented to obtain the modal characteristics. Towards this end, we choose six linearly independent shape functions in the form of product of Clamped-Free (C-F) and Free-Free (F-F) beam mode shapes. The characteristic equation for the determination of the natural frequencies is formulated. This sixth-order polynomial equation is solved numerically to obtain the natural frequencies of the rotating staggered cantilever plate. The results for the non-dimensional natural frequencies as a function of the non-dimensional rotating speed are presented in the form of natural frequency maps. Further, these results are validated using Finite Element (FE) simulation. Towards this end, a pre-stressed modal analysis is performed in ANSYS. It is noted that the results obtained by the two methods are in good correlation.