Natural frequency spectra of spatial structure
The object of the study is a diagram of a statically determinate truss in the form of a closed rectangle with vertical supporting columns along the inner contour. The structure is formed from quadrangular rod pyramids. All pyramids are united along the vertices by a square contour. Four additional horizontal ties are located at the corners of the structure. Method. Estimates of the lowest oscillation frequency of the truss are found using the Rayleigh energy method and the Dunkerley method. All mathematical transformations are performed in the Maple symbolic mathematics system. The dependence of the solution on the number of panels is obtained by generalizing a series of solutions for farms with a successively increasing number of panels. Results. The value of the first natural frequency is compared with the numerical solution obtained by analyzing the entire spectrum of natural frequencies of the vertical oscillations of the system of masses located in the truss nodes. The frequency equation is compiled and solved using the eigenvalue search operators in the Maple system. The spectrum of natural frequencies of a family of regular trusses of various orders is analyzed.