Application of graphs and structural numbers to determination of the characteristic equation and of the frequency spectrum

Topological methods based on the relationship between the set of trees of a graph and the determinant of the graph are applied to discrete linear mechanical systems. Transformations of graphs, generation of trees, and use of structural numbers figure in the treatment. A functional model and a terminal graph are employed in setting up the equation for a vibrating linear system. The relationship between the graph and the structural number can be used to arrive at the characteristic equation without having to set up the differential equations of motion of the system. The relationship between signal flow graphs, terminal graphs, and bond graphs is reviewed, along with algebraization and computerization of graph calculations with the aid of structural numbers.