Frequency spectrum of natural oscillations of the spatial structure of the rod pyramid

Строительная механика

The object of the study is a pyramid-type enclosure statically defined in space. The truss has support posts along the contour of the base. The corner buttons are fixed on the support sphere, cylinder, and bracket. Structure with axes of symmetry. The purpose of the study is to give formulas on the dependence of the deflection under the effect of uniform load and the first natural frequency of oscillation on the number of plates, size and mass concentrated at the nodes of truss. Method. By using equilibrium equations at the nodes it is possible to find the forces in the truss elements. The system of equations also includes the responses of the vertical supports located along the contour of the truss structure. From this, it can be concluded that the force distribution on the truss rods does not depend on the number of plates. The deflection and stiffness values of the truss structure are calculated according to the Maxwell–Mohr formula. The lower analytical estimate of the first frequency was obtained using 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 structures 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 natural frequency spectrum of the truss is analyzed.