The formula for the lower estimate of the fundamental frequency of natural vibrations of a truss with an arbitrary number of panels

Строительные конструкции, здания и сооружения

The object of the research is a planar, statically determinate girder of the beam type with a triple diagonal lattice.The truss mass is modeled by equal masses distributed over the nodes of the lower chord. By the Dunkerley method, under the assumption of vertical vibrations of loads, a lower analytical estimate of the first natural vibration frequency is obtained. Method. The forces in the members are calculated by cutting out nodes from the solution of a system of linear algebraic equations. Generalization of individual solutions to the case of an arbitrary number of panels is carried out by the induction method with the involvement of operators of the Maple computer mathematics system. Results. Comparison with the numerical solution found from the solution on the spectrum of natural vibrations of a multi-mass system shows that the estimation accuracy depends on the number of panels and varies from 16% for trusses with two panels to 4% for trusses with more than 11 panels. With a decrease in the ratio of the panel height to its length, the accuracy slightly increases. Based on the analysis of the derived formula, it is shown that the dependence of the first frequency on the height of the truss has a maximum. An algorithm for generalizing the solution to the case of members of different stiffness is proposed.