Formula for natural frequency oscillation truss with an arbitrary number of panels

The object of research is the problem of the first frequency of free vibrations of a planar statically determinate regular beam truss with a mass uniformly distributed over the nodes. Method. The problem is solved in the Maple computer mathematics system in symbolic form. The masses oscillate along the vertical axis. The solution is sought using the Dunkerley method. The induction method and Maple operators were used to generalize a series of analytical solutions for trusses with a successively increasing number of panels. Results. The results are compared with a numerical solution obtained as the minimum frequency of the entire frequency spectrum and a simplified version of the Dunkerley method. It is shown that the accuracy of analytical solutions increases with an increase in the number of panels. The spectra of a family of regular trusses of various orders are analyzed numerically. Spectral constants, spectral isolines, and resonant safety regions have been identified.