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Impulse Response Operators for Structural Complexes

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Research and development rept.

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A number of sequential and parallel procedures for analyzing the response complexes are discussed. The impulse response vector operator is defined by impulse response operators, each associated with a unique path between the localized position of a test drive and an observation. The drive is a vector and the response is the scalar product of the impulse response operator and the drive vectors. A sequential procedure of subdividing a structural complex into a number of coupled dynamic systems is stated in terms of matrices and vectors e.g., the response is a vector each element represents the response of a specific dynamic system, the impulse response operator is a matrix the off diagonal elements describe the couplings between the dynamic systems. The dynamic systems are chosen so each is described as an eigen impedance operator. A modal analysis is applied to the multiple dynamic systems composing the model of the structural complex. In the modal analysis the ranks of the impulse response matrix, the response vector, and the drive vector, are swollen by the modal count, rendering the matrix equation for the response unwieldy. The modal approach may be substituted by a parallel wave approach in which the propagations in the dynamic systems are described by impulse response operators that are commensurate with those pertaining to boundlessly extrapolated dynamic systems. The finiteness of the dynamic systems are accounted for by junction matrices a junction defines the boundaries through which dynamic systems interact either with each other transmission or with selfreflections. The resulting formalism is rather unwieldy.

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  • Operations Research

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