Variable Kinematic Shell Finite Elements for Dynamic Analyses of Rotating Structures

Abstract

This paper makes use of low- and high-fidelity finite plate and shell elements for vibrational analyses of various rotating structures. The two-dimensional models, developed with the Carrera Unified Formulation (CUF), are obtained by adopting two different kinematics expansions, namely the Lagrange-like (LE) and Taylor-like (TE) polynomials. The possibility of selecting different kinematic expansions enables various configurations such as composite, reinforced and sandwich structures to be considered. The equations of motion of rotors with arbitrarily shaped cross-sections are derived with respect to a co-rotating reference system. All contributions induced by the rotational speed (the Coriolis force, the spin-softening and the stress-stiffening terms) for both spinning and blade-like configurations are included in the equations of motion. Furthermore, the linearized and geometrically nonlinear approaches are presented to compute the speed-induced stiffening effect. Numerical simulations are performed on a swept-tip blade and a shallow shell to validate the formulation. Comparisons with solutions available in the literature demonstrated the accuracy of the approach.