Spatial Formulation of Elastic Multibody Systems with Impulsive Constraints

The problem of modeling the transient dynamics of three-dimensional multibody mechanical systems which encounter impulsive excitations during their functional usage is addressed. The dynamic behavior is represented by a nonlinear dynamic model comprising a mixed set of reference and local elastic coordinates. The finite-element method is employed to represent the local deformations of three-dimensional beam-like elastic components by either a finite set of nodal coordinates or a truncated set of modal coordinates. The finite-element formulation will permit beam elements with variable geometry. The governing equations of motion of the three-dimensional multibody configurations will be derived using the Lagrangian constrained formulation. The generalized impulse-momentum-balance method is extended to accommodate the persistent type of the impulsive constraints. The developed formulation is implemented into a multibody simulation program that assembles the equations of motion and proceeds with its solution. Numerical examples are presented to demonstrate the applicability of the developed method and to display its potential in gaining more insight into the dynamic behavior of such systems.