Linearized and Nonlinear Analyses of Rotating Structures Through High-Fidelity Beam/Plate/Shell Finite Elements

Abstract This work investigates the dynamic response of isotropic and composite rotating structures with various geometric and mechanical properties using low- and high-fidelity one-dimensional (1D) and two-dimensional (2D) finite element models. The adopted mathematical formalism is based on the Carrera Unified Formulation (CUF). The CUF offers a procedure to obtain higher-order beam, plate, and shell models hierarchically and automatically. These theories are obtained by expanding the unknown displacement variables over the beam cross-section or along the plate/shell thickness. Various beam, plate, and shell models can be implemented depending on the choice of the polynomial employed in the expansion. In this work, both Taylor-like (TE) and Lagrange (LE) polynomials are considered for developing different kinematic models. The finite element method (FEM) is employed to solve the geometrically linearized or fully nonlinear governing equations, including Coriolis and in-plane initial stress contributions. Various ways to derive the governing equations of axisymmetric rotors in an inertial frame of reference or structures in a co-rotating system are discussed. Relatively simple and complex rotor configurations with different boundary conditions are considered. The beam, plate, and shell solutions are compared with results from existing literature, emphasizing the effect and importance of the geometric stiffness.