Nonlinear Dynamics of Rigid and Flexible Multibody Systems

Abstract In the present paper a unified numerical approach for dynamics modeling of multibody systems with rigid and flexible bodies is suggested. The dynamic equations are second order ordinary differential equations (without constraints) with respect to a minimal set of generalized coordinates that describe the parameters of gross relative motion of the adjacent bodies and their small elastic deformations. The numerical procedure consists of the following stages: structural decomposition of elastic links into fictitious rigid points and/or bodies connected by joints in which small force dependent relative displacements are achieved; kinematic analysis; deriving explicit form dynamic equations. The algorithm is developed in case of elastic slender beams and finite elements achieving spatial motion with three translations and three rotations of nodes. The beam elements are basic design units in many mechanical devices as space station antennae and manipulators, cranes and etc. doing three dimensional motion which large elastic deflections could not be neglected or linearised. The stiffness coefficients and inertia mass parameters of the fictitious joints and links are calculated using the numerical procedures of the finite element theory. The method is called finite elements in relative coordinates. Its equivalence with the procedures of recently developed finite segment approaches is shown, while in the treatment different results are obtained. The approach is used for solution of some nonlinear static problems and for deriving the explicit configuration space dynamic equations of spatial flexible system using the principle of virtual work and Euler-Lagrange equations.