Schematic Network Research Articles

Analogies and Schematic Networks

An analytic network is defined as a topological drawing with variables (mostly unknown) assigned to its branch-points and branches, impedance-like parameters associated with the branches, and a set of rules for finding the relations between the values of the variables and the parameters. Such a network can be called the schematic network of a particular physical structure if the values of the variables and parameters of the network correspond, according to a distinct set of rules, to the values of the physical variables and parameters measured on the structure. These rules must specify some systematic way of comparing these numerical values and also the locations in structure and network with which they are associated. If two physical structures with different types of “vibrations” (i.e., electrical, mechanical, acoustical, etc.) have the same schematic network, they are analogs; they can be called direct analogs. If two structures have schematic networks which are duals, they can be called indirect analogs. The conclusions of LeCorbeiller and Yeung about duality in mechanics will be reinterpreted in this manner and contrasted with comparable conclusions for acoustical structures.