Free vibration analysis of rotating composite blades via Carrera Unified Formulation

Abstract

Carrera Unified Formulation (CUF) is used to perform free-vibrational analyses of rotating structures. CUF is a hierarchical formulation which offers a procedure to obtain refined structural theories that account for variable kinematic description. These theories are obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor’s expansions of N-order, in which N is a free parameter. Linear case (N=1) permits us to obtain classical beam theories while higher order expansions can lead to three-dimensional description of dynamic response of blades. The Finite Element Method is used to solve the governing equations of rotating blades that are derived in a weak form by means of Hamilton’s Principle. These equations are written in terms of “fundamental nuclei”, which do not vary with the theory order (N). Both flapwise and lagwise motions of isotropic, composite and thin-walled structures are traced. The Coriolis force field is included in the equations. Results are presented in terms of natural frequencies and comparisons with published solutions are provided.