Fundamental issues in frequency domain structural synthesis are addressed. A new formulation is developed which is based on a transformation of the pre-synthesis frequency response matrix. The new formulation provides an exact and orderly treatment of both substructure coupling and structural modification, and constitutes the most general statement to date of structural synthesis in the frequency domain. The new formulation accommodates structural elements of any type. Lumped and finite elements can be installed between substructures, (coupling) and as redundant load paths (modification). General linear damping is accommodated. The theory provides a thorough accounting of the role of graph theory in structural synthesis.

Additionally, a new theory for structural identification has been formulated which addresses critical issues in the airframe model improvement problem. The theory is also based on the structural synthesis transformation, which provides a natural analytic bridge between two frequency response models of a linear structural dynamic system. The theory corrects a finite element model such that its frequency response predictions precisely reproduce the corresponding test data, at all frequencies of interest. The structural synthesis transformation quantifies the difference between the two models by extracting from their matrix difference a complex and frequency-dependent frequency response error matrix. The associated error impedance matrix can then be decomposed into its constituent mass, damping, and stiffness error matrices, each calculated as a function of frequency. The theory demonstrates that an exact solution for the corrective structural matrices of stiffness, mass, and damping is available directly from spatially complete frequency response data. Furthermore, the theory reveals and accommodates the frequency dependency imposed on the identified parameters due to the use of spatially incomplete test data. Operating spatially, the theory provides an exact solution for the location of modeling errors, a capability compromised only by the requirement of dynamic reduction of the finite element description. The theory inherently provides corrections for errors due to the discretization of a continuous structure, the further discretization errors imposed by dynamic reduction of the finite element model, and accommodates frequency-dependent mechanisms in the structure. Modal analysis and modal parameter identification are completely eliminated.