Zastosowanie grafów i liczb strukturalnych do wyznaczania równania charakterystycznego i widma częstości

In the paper the authors discussed topological methods of determining the equation of state and the spectrum of frequency for linear discrete mechanical systems. Describing a vibrating system by a functional model and a therminal graph, the methods of creation of such equation were shown. Utilizing the relation between a graph and a determinant function of a structural number, the authors proved that the characteristic equation and the frequency spectrum can be found by a simpler procedure, without setting the differential equations of motion. Practical applications of methods described were demonstrated on examples.