Dependence of the fundamental vibration frequency of a semi-braced beam truss on the number of panels

The object of research is a new scheme of a flat statically determinate regular beam truss with a semi-braced double lattice. An algorithm has been developed for deriving the analytical dependence of the first natural frequency of oscillations of a truss on its size, mass, and number of panels. The mass of the truss is concentrated in its nodes, the rods are elastic, and the nodes oscillate vertically. Method. To calculate the stiffness of the truss, the Maxwell-Mohr's formula is used. Generalization of solutions to the case of an arbitrary number of panels is performed by the induction method in the Maple computer mathematics systems. Results. The solution with coefficients of the type of polynomial in the number of panels is compared with the well-known Dunkerley solution and the numerical one obtained as the first frequency of the entire frequency spectrum. It is shown that the proposed method provides not only a more compact, but also a more accurate formula for calculating the frequency. As the number of panels increases, the accuracy of the analytical solution increases.