Dependence of the Two-Span Truss Bridge Vibration Frequency on the Number of Panels

The object of the research is a planar, externally statically indeterminate truss with a cross-shaped lattice. The truss has supports at the ends and in the middle. The dependence of the lowest frequency of vibrations of the truss is found under the assumption that the mass of the structure is concentrated in its nodes. Both horizontal and vertical displacements of nodes are taken into account. Method. The reactions of the supports and the forces in the rods are found in an analytical form by the method of cutting nodes in the Maple computer mathematics system. The stiffness matrix is calculated using the Maxwell-Mohr formula. The results of calculating the first natural frequency by the Dunkerley method of a series of solutions for trusses with a different number of panels are generalized by induction to an arbitrary number of panels. Results. A comparison of the analytical expression for the first frequency with the lowest value of the natural oscillation spectrum obtained numerically shows the high accuracy of the derived formula. It is noted that with an increase in the number of panels, the accuracy of the approximate analytical solution increases, reaching several percent with the number of panels in each span of more than twenty.