Kinematic analysis, spectrum of natural frequencies, and formula for the first frequency of a planar truss

The object of research is the statically determinate regular symmetrical rectangular beam truss with a double lattice fixed on two supports. The lower chord of the structure is curvilinear, with a rise in the middle of the span. The mass of the lattice is distributed over its nodes. Method. A kinematic analysis reveals the variability of the lattice for a certain number of panels. In this case, an algorithm for searching for the distribution of virtual velocities of lattice nodes is described. Using the Maple computer mathematics system, a formula is derived for the dependence of the lower estimate of the first frequency of natural oscillations of the structure on the number of panels from the range of acceptable values. The result agrees with the numerical calculation considering all degrees of freedom of the structure. It is shown that with an increase in the number of panels, the accuracy of the analytical solution increases. Spectral constants are found in the frequency spectrum of a family of regular trusses.