The natural frequency of a two-span truss

Строительные конструкции, здания и сооружения

The object of the research is a statically definable truss with two spans and a diamond-shaped lattice. One of the supports is a fixed hinge. The other two are movable. The dependence of the first natural vibration frequency of the truss on its size, mass, and also the number of panels is in analytical form. Methods. The rigidity of a structure with masses concentrated in its nodes is determined by the Maxwell-Mohr formula. The lower analytical estimate of the first frequency is calculated using the Dunkerley formula. Results. The generalization of a series of private solutions for trusses with a sequentially increasing number of panels is made by the induction method. The general terms of the sequence of coefficients are determined from the solution of linear homogeneous recurrent equations. All transformations, including finding the forces in the bars by cutting nodes, are performed in the Maple computer mathematics system. To check the solution, the entire frequency spectrum, including the lowest frequency, is in numerical form. Comparison of the analytical solution with the numerical one shows that the accuracy of the analytical estimate from below is quite high and increases with the number of panels.