Rotordynamic analyses with variable-kinematic beam and shell finite elements

Many types of machinery require components that rotate at high speeds, such as thin- and thick-walled cylinders. Consequently, knowledge of the dynamics of these rotating parts is a crucial part of the design process of the whole system. Therefore, numerical models developed for rotodynamic analyses should predict the mechanical response accurately under various operational conditions by including as many details as possible. This work investigates the dynamic response of isotropic and composite rotating cylindrical 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 and shell models hierarchically and automatically. These theories are obtained by expanding the unknown displacement variables over the beam cross-section or along the shell thickness. Various beam 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 equations of motion, including Coriolis and in-plane initial stress contributions. Various thick and thin cylinders with different boundary conditions are considered. The beam and shell solutions are compared with the three-dimensional ones from the literature, emphasizing the effect and importance of the geometric stiffness.