Formulas for the first two frequencies of natural oscillations of a regular truss

The object of research is the frequencies of natural oscillations of a regular spacer flat lattice truss. The mass of the truss is conventionally located at its nodes. Only small vertical oscillations of the masses are considered. The rods of the structure are assumed to be linearly elastic. Method. The modified Dunkerley method is used to derive the formula for the dependence of the first natural frequency of the truss free oscillations. For the second frequency, the form of dependence on the number of panels is taken from the solution of the problem of the first frequency with correction factors that are calculated from the numerical solution by the collocation method at three points. Results. For the first two frequencies of truss oscillations, compact calculation formulas for the dependence on the number of panels are obtained, allowing one to estimate oscillations of a truss with an arbitrary number of panels without loss of accuracy. For an odd number of panels in half a span, the kinematic variability of the structure was discovered and confirmed by the distribution of velocities.