Linear dynamics of flexible multibody systems

Abstract

We present a new methodology to derive a linear model of flexible multibody system dynamics. This approach is based on the two-port model of each body allowing the model of the whole system to be built just connecting the inputs/outputs of each body model. Boundary conditions of each body can be taken into account through inversion of some input-output channels of its two-port model. This approach is extended here to treat the case of closed-loop kinematic mechanisms. Lagrange multipliers are commonly used in an augmented differential-algebraic equation to solve loop-closure constraints. Instead, they are considered here as a model output that is connected to the adjoining body model through a feedback. After a summary of main results in the general case, the case of planar mechanisms with multiple uniform beams is considered, and the two-port model of the Euler-Bernoulli beam is derived. The choice of the assumed modes is then discussed regarding the accuracy of the first natural frequencies for various boundary conditions. The overall modeling approach is then applied to the well-known four-bar mechanism.

Finite element based N-Port model for preliminary design of multibody systems

“…This first assumption does not constrain the dynamic analysis to the clamped-free condition as already demonstrated in Ref. [33] for an homogeneous beam, but it allows simplifying Eq. (7) without any loss of information and studying any kind of boundary conditions.…”

“…(6) (13) This model, conceived with the clamped-free condition, is useful to study any other kind of boundary configuration as proved in Ref. [33] thanks to the invertibility of all of its 12 input-output channels. Moreover the TITOP model allows us to directly link several sub-structures of an open/closed chain-like complex body.…”

“…Thanks to the fact that a residual mass of the sub-structure  i is associated with nodes P and C by FEM synthesis, all the 12 input-output channels are invertible. The single-channel inversion procedure is described in Appendix 1 of [33].…”

“…Chebbi [33] completed the formulation by presenting a rigorous comparison of the TITOP model of a uniform beam, the same stated in Ref. [29], for several boundary conditions, with results provided by the Euler-Bernoulli theory.…”

A Novel Dynamic Model of a Reaction Wheel Assembly for High Accuracy Pointing Space Missions

“…The advantage of this method is to be modular and appropriate for control/structure co-design. The TITOP approach is applied in [4] to study any flexible multi-body system with closed-loop kinematic chains and in [5] to model flexible solar panels considered as bending plates connected to a spacecraft main body.…”