An algebraic algorithm for the design and analysis of linear dynamical systems

Munjal, M. L. ; Sreenath, A. V. ; Narasimhan, M. V. (1973) An algebraic algorithm for the design and analysis of linear dynamical systems Journal of Sound and Vibration, 26 (2). pp. 193-208. ISSN 0022-460X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00224...

Related URL: http://dx.doi.org/10.1016/S0022-460X(73)80231-7

Abstract

In an earlier paper [1], it has been shown that velocity ratio, defined with reference to the analogous circuit, is a basic parameter in the complete analysis of a linear one-dimensional dynamical system. In this paper it is shown that the terms constituting velocity ratio can be readily determined by means of an algebraic algorithm developed from a heuristic study of the process of transfer matrix multiplication. The algorithm permits the set of most significant terms at a particular frequency of interest to be identified from a knowledge of the relative magnitudes of the impedances of the constituent elements of a proposed configuration. This feature makes the algorithm a potential tool in a first approach to a rational design of a complex dynamical filter. This algorithm is particularly suited for the desk analysis of a medium size system with lumped as well as distributed elements.

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