Linear dynamics of flexible multibody systems

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.