Three-Dimensional Elasticity-Based Solutions for Natural Vibrations of Low Aspect Ratio Compressor Blades

This paper offers three-dimensional (3-D) vibration frequency solutions for low aspect ratio compressor blades. The Ritz method is used to minimize the 3-D elasticity-based dynamical energies with displacements approximated by mathematically complete polynomials satisfying the clamped boundary conditions exactly. The accuracy of the method is established by a convergence study explicitly showing the influence of solution determinant size. Several tables are presented which show the variation of natural frequencies with twist angle in the presence of skewness of low aspect ratio compressor blades. Results obtained using the present Ritz method are used to elucidate those frequency solutions which are inaccessible using beam, plate and shell theories, since kinematic constraints associated with these theories are eliminated in the present 3-D approach.