Influence of geometric nonlinearities in the dynamics of flexible treelike structures

Abstract

A comprehensive computer algorithm used in the dynamic analysis of multibody systems is presented. The procedures developed combine Kane's equations, the strain energy, and modal analysis to describe the elastic bodies. The equations of motion are expressed in a form in which their coefficients are based on the partial velocity and partial angular velocity arrays and are easily coded for computers. The nonlinear geometric stiffness matrix is developed for three-dimensional beams that account for the couplings between the deformation components having significant effects in high-speed systems. The method presented in this paper is tailored for structures with variable cross-sectional beam elements such as spacecraft antennae, helicopter rotor blades, robot systems, and mechanisms. The effects of rotary inertia as well as shear deformation are automatically included into the equations of motion. A method for obtaining the shape function matrix consisting of assumed dynamic modes is also presented. In addition, the preceding formulations are used in a simulation of a space-based robotic manipulator, and the results are compared with those obtained by Kane et al. in Ref. 20.