Flexural Vibration of Pretwisted Tapered Cantilever Blades

Abstract

The Ritz-Galerkin process is used to solve the two coupled differential equations of motion of a pretwisted tapered cantilever blade vibrating in flexure. A five-term solution for each y and x deflection satisfying the boundary conditions is found to give accurate values for the first three modes of a uniform beam. Using these five-term solutions the first five coupled frequencies of pretwisted tapered cantilever blades are determined and compared with experimental values of some typical blades. The theoretical values of frequencies obtained are shown to be in favorable agreement with the experimental values.