Dynamic modeling of flexible bodies in multibody systems.

Abstract

The objective of this research is the development of analytical and computational methods for analyzing the effects of motion-induced stiffness variations on the dynamic behavior of mechanical multibody systems composed of structural components undergoing arbitrarily large, unrestrained, overall motions as well as small elastic deformations. The importance of the subject is indicated by the fact that components of dynamic multibody mechanical systems are often assumed to possess nearly constant stiffness properties, even though rather benign overall motions can, in some important applications, cause enough variation in stiffness to have dramatic effects on dynamic behavior. Thus, incomplete accounting for such variations can yield completely erroneous analysis results. As newer designs for spacecraft, robotic manipulators, and mechanisms call for lighter weight and faster operational speeds, the topic assumes even greater importance as characteristic stiffnesses vary significantly for these extremely flexible systems. The focus of the present research is the study of structural stiffness variations caused by inertia forces and torques, a main goal being to formulate an efficient and effective technique for accounting for all such stiffness changes in a general multibody simulation theory which incorporates flexible body control schemes and arbitrary forcing functions. This study is carried out by two modeling methods: (1) extensive use of geometric constraints imbedded in Rayleigh-Ritz assumed mode techniques along with consistent linearization schemes and linear strain-displacement relationships; and (2) nonlinear strain-displacement modeling based on von Karman strain measures. The modeling methods are applied to beam and plate structures undergoing various translational and rotational motions. Numerical examples are solved for the purpose of demonstrating the accuracy of the modeling methods.