Dependence of the First Frequency of Natural Vibrations of a Beam Truss with a Triangular Lattice on the Number of Panels

Abstract

An algorithm is given for deriving the analytical dependence of the smallest natural frequency of oscillations of a plane of a statically determinate regular truss on the number of panels. The Dunkerley method and the simplified version Dunkerley method are used. It is shown that the simplified version gives not only a simpler, but also a more accurate formula. It is assumed that the mass of the truss is concentrated on its nodes, and the number of degrees of freedom of the structure coincides with the number of the nodes. For analytical transformations and to solve recurrent equations, the computer mathematics system Maple was used. Truss stiffness is calculated using the Maxwell–Mohr formula.