The formula for the fundamental oscillation frequency of a planar spacer truss

The object of research is an externally statically indeterminate spacer-type truss, which has a flat structure with a diamond-shaped lattice. Both supporting hinges of the truss are motionless. The support rods are assumed to be rigid. In analytical form, the dependence of the first natural frequency of oscillations of the truss on its size, mass, and number of panels is found. Method. The stiffness of a truss with masses concentrated at the nodes is determined by the Maxwell-Mohr formula under the assumption that the stiffnesses of all rods are the same. An analytical estimate of the first frequency was calculated using the Dunkerley formula. A generalization of a series of solutions for farms with a successively increasing number of panels was carried out by the induction method. The common terms of the sequence of coefficients are found from the solution of linear homogeneous recurrent equations. All transformations, including calculation of forces in rods and reactions of supports, were performed in the Maple computer mathematics system. Results. The dependence of the natural frequency on the number of farm panels was found in numerical form. A comparison of the analytical solution with the numerical one showed that the accuracy of the analytical estimate from below increases with the number of truss panels.