The first frequency and frequency safety area of a cantilever truss with an arbitrary number of panels

The object of research is a planar model of a statically determinate truss system. Method. The rigidity and first natural frequency of oscillations of the truss are analyzed analytically. If the truss rods have the same cross-section, and the mass of the truss is evenly distributed among its nodes, then each mass has one degree of freedom, and the stiffness of the rods is the same. Using induction, analytical expressions for the deflection are found. The formula for the dependence of the main (first) natural frequency of oscillations of the truss on the number of panels is derived by the Dunkerley method. Based on the results of calculating deflections in a series of similar trusses with different numbers of panels, the expected dependence of deflections on the load, elastic properties of the rods and the number of panels was obtained. The solution of the system of linear equations that determine the force in the rods and any transformations are performed in the Maple computer mathematics package. Using the Maxwell-Mohr formula, the stiffness matrix of the structure can be determined. Results. The first natural frequency of the truss obtained by the analytical method is compared with the results of the numerical method. The frequency spectrum of the truss was analyzed, and conclusions were drawn about the dependence on the size of the panels. In the combined frequency spectrum of a family of regular trusses, a region of unattainable frequencies is identified.