Analytical calculation of an externally statically indeterminate truss oscillation frequency

The research object is a planar braced jointed frame with a cross-shaped double lattice. The mass of the truss is evenly distributed across its nodes. The task is to obtain an analytical dependence of the fundamental frequency of the frame's vibrations on its dimensions, mass, and number of panels. Method. The frame is statically determinate. The method of cutting nodes is used to determine the forces in the rods and the reactions at the supports. The stiffness of the structure is calculated using the Maxwell - Mohr formula. The simplification of the frequency calculation for systems with many degrees of freedom is achieved by applying the Dunkerley method. Results. Compact formulas for the deflection of the frame and its natural frequency of vibration have been obtained. A case of kinematic variability of the structure with an odd number of panels in half the span was discovered. A comparison of the analytical result with the numerical one shows good accuracy of the proposed method. Some asymptotic solutions have been found. © The Author 2025