Resonance safety zones of a truss structure with an arbitrary number of panels

The dependence of the resonant safety zone on the dimensions of the truss rods is analyzed in detail by studying a statically defined symmetrical beam truss. In this problem, it is assumed that the truss rods have the same cross-section, and the mass of the truss is uniformly distributed between its nodes, so each mass has one degree of freedom, and the stiffness of the rods is the same. Method. Using the induction method, analytical expressions were found for the deflection of the truss, from which the expected dependence of the deflection on the load and elastic properties of the rods and the number of panels was obtained. Using the Dunkerley method and its simplified version, a formula was obtained in analytical form for the dependence of the first natural frequency of oscillations on the number of panels. In this study, all transformations were performed using the Maple mathematical language program. Results. To evaluate the accuracy of the proposed methods, the results obtained by the analytical solution are compared with the results of the numerical method so that its suitability in solving the problem of trusses with many panels can be assessed. In addition, the natural frequency spectra, presented in the form of a graph, were analyzed and conclusions were drawn about the dependence on the size of the panels.