Formula for the Dependence of the Fundamental Natural Frequency of a Regular Truss on the Number of Panels

The object of study is a planar model of a symmetrical statically defined frame truss. The truss rods have the same cross-section and the truss mass is evenly distributed among its nodes. Using the Maxwell–Mohr formula, the stiffness matrix of a statically defined structure can be determined. The purpose of the study is to obtain formulas for the dependence of the first natural frequency of vibration of the truss under consideration on the number of panels. Generalization of particular solutions for trusses with different numbers of panels to the general case is carried out using the induction method. To estimate the first frequency of the truss, the Dunkerley method and its simplified version were used. All transformations in the study were performed analytically using the Maple computer mathematics system. The first natural frequency of the truss obtained by analytical methods is compared with the results of the traditional numerical method. The results show that as the number of panels increases, the accuracy of the analytical assessment increases.