Natural Frequency Spectrum and Fundamental Frequency Formula for Plane Periodic Lattice Truss

The goal is to determine the free vibration natural frequency spectrum for a plane statically determinate truss with a cross-shaped lattice. The truss members are elastic and have the same stiffness. Both truss supports are pinned; the truss is externally statically indeterminate. A model, in which the mass of the structure is uniformly distributed over its nodes, and their vibrations occur vertically, is considered. The Maxwell-Mohr method is used to determine the stiffness of the truss. The member forces included in the formula are calculated by the method of joints using the standard operators of Maple mathematical software in symbolic form. The eigenvalues of the matrix for trusses with different numbers of panels are determined using the Maple system operators. Spectral constants are found in the overall picture of the frequency distribution constructed for trusses of different orders. A formula for the relationship between the first frequency and the number of panels is derived from the analysis of the series of analytical solutions for trusses of different orders. A simplified version of the Dunkerley method is used for the solution, which gives a more accurate approximation in a simple form. The relationship between the truss deflection under distributed load and the number of panels was found. Spectral constants were found in the frequency spectrum.