Flexible Multibody Systems, Numerical Analysis Of The Dynamic Stiffening

In flexible multibody systems, the rotation of some parts with little specific gravity at high speed always cause the phenomenons of dynamic stiffening. At this time, the effect of elastic movement of parts on dynamic behavior of systems can't be ignored. Factually, because the deformation of most of the elastic parts are very little, the linear finite element theory is often used to establish dynamic model in the classical multibody system theory, and coupling of space movement in large scale and elastic deformation of parts is ignored. The dynamic stiffening is exactly caused by such coupling.In this article, several existing main compensation methods for the term of dynamic stiffening are reviewed; describing method of material coordinate is introduced on the basis of the principle theorem of mechanics of continuum; and the dynamic equation of flexible body is derived from nonlinear Green strain tensor and Kichhoff stress tensor, which are based on initial configuration. Anew compensation method, 'Belated initial stress method', is developed for term of dynamic stiffening by synthesizing the existing method. The main idea of this method is using internal stress of last moment to construct the term of dynamic stiffening caused by rotation at high speed. Then the effect of dynamic stiffening can be simulated at lower cost when the equation of motion of elastic parts is linear.In the article, the flexible multibody system on the plane is researched; the coupling dynamic model with relative accuracy is established; and the phenomenon of dynamic stiffening is simulated by 'belated initial stress method when the parts are rotating at high speed.