Accurate Nonlinear Dynamics and Mode Aberration of Rotating Blades

Abstract

Nonlinear dynamics and mode aberration of rotating plates and shells are discussed in this work. The mathematical formalism is based on the one-dimensional (1D) Carrera unified formulation (CUF), which enables to express the governing equations and related finite element arrays as independent of the theory approximation order. As a consequence, three-dimensional (3D) solutions accounting for couplings due to geometry, material, and inertia can be included with ease and with low computational costs. Geometric nonlinearities are incorporated in a total Lagrangian scenario and the full Green-Lagrange strains are employed to outline accurately the equilibrium path of structures subjected to inertia, centrifugal forces, and Coriolis effect. A number of representative numerical examples are discussed, including multisection blades and shells with different radii of curvature. Particular attention is focused on the capabilities of the present formulation to deal with nonlinear effects, and comparison with s simpler linearized approach shows evident differences, particularly in the case of deep shells.