Condensed stiffness matrices to study vibrations in multibody systems

The problem of model reduction is necessary for a more concise dynamic description of complex mechanical systems. In dynamics of structures the dynamic behaviour is expressed considering both the static modes at the boundaries of a domain and the clamped modes of the internal when the boundary nodes are fixed. This method is used to obtain a reduced impedance matrix from a larger mechanical impedancematrix and to create a superelement, that is a subsystem able to interconnect to other superelements at the boundary nodes which takes into account its inner dynamics through a number of normal modes. In this paper, a novel Component Mode Synthesis method, called Augmented Component Mode Synthesis method is proposed. Despite the common procedure to create superelements to be combined by means of joints; here, the joints are included in the reduction procedure. This novelty allows to obtain larger superelements that might be subparts of a mechanism or even the whole mechanism. Following a method similar to the well-known Craig-Bampton method, the fixed-interface normal modes and interface constraint modes are defined including the joints contribute. Then, the transformation matrix necessary to obtain the reduced stiffness and inertia matrices is presented. Finally, the case study of a two-beam frame is presented to demonstrate the feasibility of the proposed method and its validity.