The natural frequency of a truss with double braces

Строительные конструкции, здания и сооружения

The object of study is a statically determinate plane regular truss with parallel belts. The derivation of the formula for the dependence of the first natural oscillation frequency of the truss on the number of panels and the rigidity of one of the support links is given. Method. The forces in the rods are determined in symbolic form by cutting out nodes from the solution of a system of linear equations in the Maple computer mathematics system. The system of equations includes both the forces in the rods and the reactions of the supports. The masses concentrated in the truss nodes have two degrees of freedom. To determine the rigidity of the structure, the Maxwell-Mohr formula is used. Based on a series of separate analytical solutions for trusses with a different number of panels, a general solution is obtained by induction, which is valid for any number of panels. Analytical transformations and numerical solution of the spectrum problem are carried out in the Maple symbolic mathematics system. Results. Comparison of the found analytical results with the numerical solution of the problem of the spectrum of natural oscillations of a system with a finite number of degrees of freedom shows its high accuracy, which grows with an increase in the number of panels.