Abstract
Generally speaking, the mechanical systems can be classified into two main groups: open-loop and closed-loop systems. In this investigation, a recursive method is developed for the dynamic analysis of open-loop flexible systems. The nonlinear generalized Newton-Euler equations are developed for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The method to solve equations of motion for open-loop systems consisting of interconnected rigid and flexible bodies is presented in this paper. This method applies recursive method with the Newton-Euler method for flexible bodies to obtain a large, loosely coupled system equation of motion. In this paper, the computer implementation of dynamic analysis method in flexible multibody dynamics is described. The computational procedures which are used to automatically construct and numerically solve the system of loosely coupled dynamic equations expressed in terms of the absolute and joint coordinates are discussed. This computer program consists of three main modules: constraint module, mass module and force module. The constraint module is used to numerically evaluate the relationship between the absolute and joint accelerations. The mass module is used to numerically evaluate the system mass matrix as well as the nonlinear Coriolis and centrifugal forces associated with the absolute, joint and elastic coordinates. The force module is used to numerically evaluate the generalized external and elastic forces associated with the absolute, joint and elastic coordinates. Computational efficiency is achieved by taking advantage of the structure of the resulting system of loosely coupled equations. The absolute, joint and elastic accelerations are integrated forward in time using direct numerical integration methods. The absolute positions and velocities can then be determined using the kinematic relationships. The solution techniques used to solve for the system equations of motion can be more efficiently implemented in the vector or digital computer systems. The algorithms presented in this investigation are illustrated by using cylindrical joints that can be easily extended to revolute, slider and rigid joints. The nonlinear recursive formulations developed in this paper are demonstrated by a numerical example.
