Simplified Dunkerley method for estimating the first oscillation frequency of a regular truss

Structural mechanics

The object of study is a planar statically determinate truss with descending braces in the lattice. The task is to obtain a simplified formula for the dependence of the first natural oscillation frequency of the truss on the number of panels. It is assumed that the mass of the truss is concentrated in its nodes. The nodes perform vertical vibrations, the stiffness of all truss rods, including rods that model supports, is the same. Method. To determine the forces in the elements, the knot cutting method is used. The rigidity of the structure is calculated using the Maxwell – Mohr formula. The sum included in the Dunkerley method is replaced by an approximate formula, which greatly simplifies the solution. Results. A simple formula is obtained for estimating the first vibration frequency of a truss with an arbitrary number of panels. It is shown that the accuracy of the proposed method is higher than the accuracy of the original Dunkerley method and increases with the number of panels.