Deformations and natural frequency spectrum of a planar truss with an arbitrary number of panels

Строительная механика

The object of the study is a planar, statically determined lattice truss on two supports. The lower belt of the contour structure is an isosceles trapezoid. The task is to obtain formulas for the dependence of the deflection and lower limit of the truss natural frequency on the number of panels. To obtain the deviation value, the Maxwell – Mohr formula is used. The forces in the rods are determined in a conditional form by cutting out nodes from the solution of a system of linear equations in the Maple computer mathematics system. The system of equations includes both the forces in the rods and the reactions of the supports. Analytical expressions for the lower limit of the truss natural frequency is found using the Dunkerley formula and the induction method for an arbitrary number of panels. It is assumed that the mass of the truss is concentrated in its nodes, each having one degree of freedom, and the rigidity of the rods is the same. Based on the results of deflection calculations in a series of similar trusses with different numbers of panels, the desired dependence of deflection on load, elastic properties of rods, and the number of panels is derived. In this paper, a linear asymptote of the deflection problem is found. The analytical frequency estimate is compared with the lowest frequency of the entire frequency spectrum found numerically. Regularities in the distribution of frequencies in the spectrum of trusses of various orders are found.