A general theory for frequency domain structural synthesis

Abstract

Fundamental issues in frequency domain structural synthesis are addressed. A new derivation of the operative synthesis equation which is based on a congruent transformation of the pre-synthesis frequency response matrix is developed. That this transformation is intrinsic to the theory is evident in the form of this operative equation found in virtually all prior references to the theory. The structure of the operative equation facilitates its straightforward incorporation into a finite element analysis environment. The new formulation provides an exact and orderly treatment of both “coupling”, the joining of previously uncoupled structures, and “modification”, the creation of redundant load paths in a structure, and makes plain their equivalence with respect to the derivation and application of the theory. The new formulation encompasses previously addressed capabilities of the theory, and provides new capabilities. A primary feature of the new formulation is the provision for general indirect synthesis, the inclusion of intermediate or interconnecting structural elements of any type. Lumped elements as well as distributed (finite) elements can be included, either between substructures in a coupling operation, or as redundant load paths in a single structure, in a modification. The application of graph theory to structural synthesis gives rise to Boolean and non-Boolean mapping matrices which organize the coupling force sign conventions. The new theory provides a thorough accounting for the role of graph theory in structural synthesis, and a fundamental understanding of the relationship between a given structural element and its mapping matrix is achieved.