A Modal Synthesis Method Based on Analytical Eigensolutions of the Substructures with Condensation of Modal Degrees of Freedom.

A modal method for the calculation of natural frequencies and mode shapes of large linear structures is presented. In order to reduce the number of modal degrees of freedom, the influence of the higher-order substructure modes is estimated by static and dynamic condensation to master model degrees of freedom. Analytical substructure eigensolutions are used which yield a reduced eigenvalue problem of the structure without any structure or substructure discretization. The method is applied to a frame structure of slender, straight beams with a lumped mass. The results are compared with finite element solutions and experimental studies. The influence of the number of substructure modes used in the modal synthesis procedure on the accuracy of the approximated structure natural frequencies is discussed