A Generalized Component Mode Synthesis Approach for Multibody System Dynamics Leading to Constant Mass and Stiffness Matrices

Abstract

A standard technique to reduce the system size of flexible multibody systems is the component mode synthesis. Selected mode shapes are used to approximate the flexible deformation of each single body numerically. Conventionally, the (small) flexible deformation is added relatively to a body-local reference frame, which results in the floating frame of reference formulation (FFRF). The coupling between large rigid body motion and small relative deformation is nonlinear, which leads to computationally expensive non-constant mass matrices and quadratic velocity vectors. In the present work, the total (absolute) displacements are directly approximated by means of mode shapes, without a splitting into rigid body motion and superimposed flexible deformation. As the main advantage of the proposed method, the mass matrix is constant, the quadratic velocity vector vanishes and the stiffness matrix is a co-rotated constant matrix. Numerical experiments show the equivalence of the proposed method to the FFRF approach.