A method for selecting deformation modes in flexible multibody dynamics

In multibody dynamics one may use a number of mode shapes for each body to capture flexibility effects. If a co‐rotational and co‐translational formulation is applied, rigid body motions are described using special generalized co‐ordinates for reference frames and such motions cannot therefore be spanned by the chosen set of mode shapes. Constraint modes are attractive to use following the FEM direct stiffness appraoch and can give accurate solutions with a minimum number of mode shapes in static and low frequency excitation problems. A set of constraint modes often span rigid body motions. The objective of this paper is to show the usefulness of combining constraint modes with an orthogonalization and subsequent rigid body mode shape rejections. In this way the remaining deformation modes together with the reference frame generalized co‐ordinates span the solution space of the original set of constraint modes. Two numerical examples are included. A simulation of a truck frame vehicle passing a bump was carried out. A rotating structure with positioning PID‐control was studied.