ФОРМУЛА ДЛЯ НИЖНЕЙ ОЦЕНКИ ПЕРВОЙ ЧАСТОТЫ СОБСТВЕННЫХ КОЛЕБАНИЙ ФЕРМЫ ТРЕХГРАННОЙ БАШНИ

Abstract

A scheme of a statically determinate tower-type spatial truss is proposed. Three lateral faces of the structure have double diagonal lattices, from below the truss rests on six racks and three additional horizontal lateral braces. The problem of the first natural frequency of free oscillations of the structure is solved. The inertial properties of the truss are modeled by the masses in its nodes. Each mass has two horizontal degrees of freedom. To obtain an analytical expression for the dependence of the lower limit of the oscillation frequency on the number of panels, the approximate Dunkerley method is used. The forces in the truss rods are found from the solution of the system of equilibrium equations for the nodes. The matrix of the system of equations is compiled in the Maple computer mathematics system. The rigidity of the structure is determined using the Mohr integral. A series of solutions obtained for a different number of panels is generalized to an arbitrary case by induction. For sequences of coefficients in the solution, linear recurrent equations are compiled and solved. The analytical solution is compared with the numerical solution of the problem of the vibration spectrum of the structure. It is shown that the first frequency of the spectrum is higher than the analytical estimate by no more than 30%. The accuracy of the estimate depends to a greater extent on the number of panels. As the number of panels increases, the accuracy of the resulting estimate increases. A trusses with only an even number of panels are considered. It is noticed that with an odd number of panels, the determinant of the system of equilibrium equations of nodes vanishes, which indicates the kinematic degeneration of the structure.