ЗАВИСИМОСТЬ ОСНОВНОЙ ЧАСТОТЫ СОБСТВЕННЫХ КОЛЕБАНИЙ ПЛОСКОЙ ШПРЕНГЕЛЬНОЙ ФЕРМЫ ОТ ЧИСЛА ПАНЕЛЕЙ

Abstract

A scheme of a statically determined planar truss with downward braces and truss reinforcement is proposed. The problems of the lower and upper boundaries of the main natural frequency of free oscillations of the structure are solved. A model with masses concentrated at the nodes is adopted. To find the formula for the dependence of the oscillation frequency limits on the number of panels, the Dunkerley and Rayleigh methods are used. The expressions for the forces in the truss rods are found from the solution of the system of linear equilibrium equations for all nodes. To obtain the matrix of the system of equations, Maple computer mathematics operators are used. The rigidity of the structure is calculated using the Maxwell – Mohr formula. The sequence of solutions obtained for trusses with different numbers of panels is generalized by induction to an arbitrary case. For the coefficients of the formula in the desired solution, homogeneous linear recurrent equations are compiled and solved. The obtained solution is compared with the numerical solution of the problem of the oscillation spectrum of a structure with many degrees of freedom. It is shown that the first frequency of the spectrum is close to its analytical estimate. With an increase in the number of panels in the truss, the accuracy of the derived formulas increases.