The dependence of the natural oscillation frequency of the console truss on the number of panels

The object of research. The object of the study is a spatial cantilever statically definable truss consisting of three planar trusses with a cross lattice system connected on the long sides. The supports of the truss structure, represented by a rack, spherical and cylindrical connection, are rigid. The rods are assumed to be elastic. The hinges connecting the rods are perfect. The dependence of the first natural frequency of vibrations of the truss on the number of panels, dimensions, weight, construction and material properties is found in an analytical form. Method. The rigidity of the truss structure with masses concentrated in the nodes is calculated according to the Maxwell-Mohr formula. Using the Dunkerley method, which gives a lower estimate of the natural frequency, the problem of deriving the analytical dependence of the lowest oscillation frequency of the console truss on a number of parameters is solved. The common terms of the sequence of coefficients are determined by solving linear homogeneous recurrent equations. To calculate the forces in the rods and analyze the results obtained, the induction method was used. All transformations, solutions of systems of equilibrium equations of nodes are made using the symbolic mathematics system Maple. Results. The analysis of the obtained results and their comparison shows the high accuracy of the formula derived using the Dunkerley method, which gives a lower estimate of the natural frequency. The analytical dependence of the accuracy of the lower estimate of the natural oscillation frequency of the cantilever truss on the number of panels is obtained.