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 rigid and flexible bodies interconnected by revolute, prismatic, free, and fixed joints. Geometrically nonlinear deformation of flexible bodies is included 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 resulting formulation generates 2ndof+m first order ordinary differential equations directly where ndof is the smallest number of system degrees of freedom that can completely describe the system configuration and m is the number of loop closure velocity constraint equations. The equations are integrated numerically in the time domain to propagate the solution.Flexible bodies are discretized using a finite element approach. The mass and stiffness matrices for a six-degree-of-freedom planar beam element are developed including mass coupling terms, rotary inertia, centripetal and Coriolis forces, and geometric stiffening terms.The formulation is implemented in the general purpose multibody dynamics computer program flxdyn. Extensive validation of the formulation and corresponding computer program is accomplished by comparing results with analytically derived equations, alternative approximate solutions, and benchmark problems 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 problems including a sliding pendulum, seven link mechanism, flexible beam spin-up problem, and flexible slider crank mechanism.