The first natural frequency of a planar regular truss. Analytical solution

The object of study is the natural oscillations of the rod structure. The first (lowest) oscillation frequency of a flat truss of a regular type is calculated by the Dunkerley method, which gives the lower frequency limit, the Rayleigh method (upper limit), and the simplified Rayleigh formula. Method. The rigidity of the structure is found by the Maxwell-Mohr formula. The stiffness of the rods is the same; the truss nodes are endowed with masses that oscillate vertically. The sum included in the denominator of the Rayleigh formula in the simplified approach is replaced by the value obtained from the deflection with the largest value (at the middle of the span). Results. Compact formulas give the first frequency value for an arbitrary number of panels. It is shown that the simplified Rayleigh method gives a compact formula and good accuracy, which increases with the number of panels.