Flexible Multibody Dynamics: Efficient Formulations with Applications

This book demonstrates how to formulate the equations of motion of complex flexible multibody systems. The book has a clear focus on the computational efficiency of the algorithms. It provides numerous interesting applications, from tethered satellites, to ground tests of spacecraft antenna deployment, to cable deployment from a ship under-water device. The book uses Kane’s method for formulating equations of motion for two reasons: reduction in labor required to derive the equations, and the simplicity of the resulting equations. The book provides computationally efficient algorithms like one producing a block-diagonal mass matrix for the dynamics of flexible body systems, including constrained flexible multibody systems. It compares solutions predicted by the theory of a closed chain of flexible bodies with experimental data. Algorithms with numerical operation counts of order-n for an n degree of freedom discretized system representing the extrusion of beams and cables are given. For beams with large deflections, the order-n solution with rigid element is shown to be as accurate as those obtained from nonlinear finite element theory, while requiring far less computation time. The book uses Kane’s method of direct linearization without deriving the nonlinear equations and applies it to the dynamics of beams and plates undergoing large rigid body motion and small vibration. For arbitrarily general structures, the book shows how errors of premature linearization due to the use of vibration modes can be compensated by geometric stiffness due to a set of inertia loads. The book gives a comprehensive review of structural dynamics and provides recursive methods of treating a variable number of bodies during deployment of cables for underwater vehicles and retraction of beams, and efficient methods of simulating flexible rocket dynamics. Finally, a theory of spacecraft dynamics with large amplitude fuel slosh is given with numerical results for various fill fractions of the fuel. Flexible Multibody Dynamics will be of interest to graduate students of mechanical engineering, aerospace engineering, applied mechanics, and spacecraft dynamics. It will be of crucial help for industry professionals doing dynamics for engineering analysis.