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ANALYSIS OF THE FREQUENCIES OF LOAD OSCILLATIONS, DEPENDING ON ITS POSITION IN THE NODES OF PLANAR TRUSS

A beam statically determinate truss with an arbitrary number of panels, in one of the nodes of which there is a massive load, is considered. The mass of the rods of the truss is neglected. A formula is derived for the dependence of the vibration frequency of the load on the hinge number in which it is located. The rigidity of the truss in the frequency equation is determined by the Maxwell-Mohr's formula. Forces in rods are determined in symbolic form by cutting out nodes in a program written in the computer mathematics system Maple. By a method of double induction (by the number of the node where the load is located and the number of panels), a series of particular solutions is generalized to an arbitrary case. A recurrence equation that is satisfied by a sequence of coefficients of particular solutions is given by a special operator of the Maple system.