A two-field approach to multibody dynamics of rotating flexible bodies

Abstract

A two-field version of the floating frame-of-reference approach is developed to describe the dynamics of a flexible body in the case of motion in a uniformly rotating frame. Full decoupling of the kinetic energy results from splitting of the motion into rigid-body modes of the floating center of mass and a velocity field orthogonal to them. The motion equations are developed from a canonical variational expression in which displacement and velocity fields play independent roles. They turn out to keep the same global structure as in the case of motion in an inertial frame. The discretization of all inertia terms is discussed in depth. It is also shown that, in the case of discretization of the continuum with 3D solid elements, all gyroscopic terms can be derived from a mass kernel and associated Si\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathbf{S} _{i}$\\end{document} matrices. Model reduction is proposed using the Herting–Martinez method in order to automatically satisfy orthogonality of the velocity field to rigid-body modes. Two application examples of high-speed rotating systems are developed at length to assess the efficiency of the proposed methodology.