A Theory of Substructure Modal Synthesis

A theory is presented for representing the displacements of a substructure finite-element mathematical model with a reduced number of degrees of freedom. A first or second-order approximation is used for the substructure’s modal coordinates associated with significantly larger or smaller eigenvalues than the system eigenvalues of excitation. The derived representations of the substructure displacements are capable of employing any type of substructure natural mode; free-free, cantilever or hybrid mode, and of retaining the dynamic behavior of any frequency range. It is shown that the present representations compute the system eigenvalues of interest with satisfactory accuracy, and it appears that the second-order approximation methods compute the system eigenvalues with greater accuracy than the first-order methods.