Multibody dynamics of very flexible damped systems

An efficient multibody dynamics formulation is presented for simulating the forward dynamics of open and closed loop mechanical systems comprised of r igid and flexible bodies interconnected by revolute, prismatic, free, and f ixed joints. Geometrically nonlinear deformation of flexible bodies is incl uded and the formulation does not impose restrictions on the representation of material damping within flexible bodies. The approach is based on Kane's equation without multipliers and the result ing formulation generates 2ndof + m first order ordinary differential equat ions directly where ndof is the smallest number of system degrees of freedo m that can completely describe the system configuration and m is the number of loop closure velocity constraint equations. The equations are integrate d numerically in the time domain to propagate the solution. Flexible bodies are discretized using a finite element approach. The mass a nd stiffness matrices for a six-degree-of-freedom planar beam element are d eveloped including mass coupling terms, rotary inertia, centripetal and Cor iolis forces, and geometric stiffening terms. The formulation is implemented in the general purpose multibody dynamics co mputer program FLXDYN. Extensive validation of the formulation and correspo nding computer program is accomplished by comparing results with analytical ly derived equations, alternative approximate solutions, and benchmark prob lems selected from the literature. The formulation is found to perform well in terms of accuracy and solution efficiency. This article develops the formulation and presents a set of validation prob lems including a sliding pendulum, seven link mechanism, flexible beam spin -up problem, and flexible slider crank mechanism.