Semi-analytical methods for singularly perturbed multibody system models

Multibody system models with either small masses or large stiffness terms may cause high computation time due to high frequency oscillations. A method to integrate such problems is motivated by results from singular perturbation theory which relate the solution of the ODE u̇=f(u,v),εv̇=g(u,v) with a small parameter ε>0ε>0 to the solution of the DAE u̇0=f(u0,v0),0=g(u0,v0). For most applications in multibody dynamics, the transformation of the linearly implicit second order model equations to this canonical form is not obvious because of non-diagonal mass matrices, constraints and large stiffness terms in the right hand side.In the present paper, we consider singularly perturbed second order problems with non-diagonal mass matrices and investigate scaling for large stiffness terms in flexible multibody systems taking into account the structure of second order equations. Furthermore, the approach is generalized to constrained systems. The computational savings of the proposed quasistatic approximation are illustrated by numerical test results for a flexible four bar mechanism.