Further approximations in flexible multibody dynamics

Abstract

A useful model for open chains of flexible bodies undergoing large rigid body motions, but small elastic deformations, is one in which the equations of motion are linearized in the small elastic deformations and deformation rates. For slow rigid body motions, the correctly linearized, or consistent, set of equations can be compared to prematurely linearized, or inconsistent, equations and to "oversimplified," or ruthless, equations through the use of open 4oop dynamic simulations. It has been shown that the inconsistent model should never be used, while the ruthless model should be used whenever possible. In this paper we attempt to examine in more detail the conditions under which the ruthless model is valid. Further, we will show how the ruthless model can be obtained directly, simplifying the dynamicist's task. An even simpler model (nicknamed the brutally linearized model) will be introduced in an attempt to get at the simplest model that still captures the essential features of the dynamic systems under consideration when undergoing slow rigid body motions. Finally, comparison of the different models for various test cases will be presented both analytically and through the use of numerical simulations.