Fundamental vibration frequency of a lattice truss with a lift

The research object is a statically determinate plane lattice truss with an arbitrary number of panels, additional end supports, and a small uplift. Method. Equal masses model the inertial properties of the truss at its nodes. The forces in the bars are found by cutting out nodes in the Maple analytical computing system. A modified Dunkerley method is used to calculate the structure's first natural frequency analytically. The sum in this method's formula is calculated using the mean value theorem, which significantly simplifies the calculation and the final natural-frequency formula. The average frequency is taken as the half-sum of the oscillation frequencies of the middle nodes in the lower and upper chords of the truss. The rigidity of the structure is calculated using the Maxwell — Mohr's formula under the assumption that the rigidities of all rods are the same. Results. The coefficients in the final formula are obtained as simple polynomials in the number of panels no higher than the third degree. Compared with a numerical method that accounts for all system degrees of freedom, the proposed method provides good accuracy, slightly underestimating or overestimating the frequency depending on the number of panels. The proposed algorithm can be used for other regular statically determinate planar and spatial structures.