A Unified Approach to the Analysis of Uniform One-Dimensional Distributed Systems

Abstract

Proper selection and ordering of the variables of uniform, linear, one-dimensional distributed, dynamic models are shown to simplify their analysis, particularly when several simultaneous energy flows are coupled. Symmetric and asymmetric product variables are identified in pairs, leading toward criteria for system symmetry and reciprocity and formulas for the desired transmission matrices. Standard operational matrix techniques allow the identification of generalized wave-scattering variables, leading to decoupled equations. Application of the technique is demonstrated for simple systems, counterflow heal exchangers, the Bernoulli-Euler beam, and flexible fluid-carrying tubes.