Formula for the lattice truss fundamental frequency vibration

The research object is a statically determinate planar lattice truss with an arbitrary number of panels. The design with two hinged supports allows kinematic variability for some numbers of panels regardless of the acting load. Method. As applied to a structure with an admissible number of panels, the analytical expression for the first frequency of free vibrations is derived using a simplified version of the approximate Dunkerley method. Comparison of the analytical solution with the numerical one shows its high accuracy, which increases with the number of panels. Analytical transformations were performed in the Maple computer mathematics system. Results. The formula for calculating the oscillation frequency has the form of a polynomial in the number of panels and can be used for simple evaluation of solutions obtained numerically. The algorithm for deriving the frequency formula can be used in similar problems of structural mechanics.