Efficient modal formulation for vibration analysis of solid structures with bolted joints

The global stiffness and damping properties of a structure, which consists of jointed substructures, are strongly influenced by the local non-linear characteristics of the joints, even if the deformations are small. The dynamic analysis (time integration) of such systems with direct non-linear Finite Element codes, which do not utilize a modal condensation, has the disadvantage of an unacceptably high computational effort, due to the huge number of nodal DOF's. In the literature, modal condensation techniques have been presented for linear problems. In the present contribution, an extension of the latter common mode bases is suggested in order to account for the local non-linear characteristics of the joints. For that sake, special modes, which we call joint interface modes, are added to an existing mode base in order to compute the state due to non-linear joint forces with a sufficient accuracy. The number of the additional joint interface modes is significantly smaller than the number of modes necessary for the classical Component Mode Synthesis of the structure with linearized joint conditions. Numerical examples demonstrate the potential of the suggested approach for the long-term dynamic analysis of huge FE structures with bolted joints.