Dynamic analysis of flexible multi-body systems using mixed modal and tangent coordinates

Abstract

This paper presents a mixed modal and tangent coordinate technique for computer aided analysis of flexible mechanical systems whose components undergo large translations and large rotations. In this model the configuration of a flexible component is identified by using two sets of generalized coordinates, namely rigid body and elastic coordinates. The rigid body coordinates define the location and orientation of a body axis, whereas the elastic coordinates define the displacement field of a component with respect to its body axis. The elastic coordinates are introduced by using finite element discretization to model flexible components with complex geometries. A modal analysis technique is used to identify the elastic mode shapes and to eliminate insignificant higher frequency modes. An orthonormalization of constraint Jacobian matrix associated with rigid body coordinates is used to identify the rigid body tangent coordinates. The resulting modal and tangent coordinates are used to develop an automated numerical integration scheme to solve the system differential and algebraic equations. Two numerical examples are considered to show the feasibility of dynamic analysis of flexible mechanical systems using this scheme.