Estimation of the Natural Vibration Frequency of a Triangular Mast

Строительные конструкции, здания и сооружения

The object of research is a spatial statically determine truss with the shape of a triangular pyramid with a cross-shaped lattice. One of the three pillars of the structure is a spherical joint. The other two are a cylindrical joint and a vertical post. In the analytical form, the dependence of the first natural frequency of vibrations of the truss on its size, mass, and number of panels is found. Method. The stiffness of a truss with masses concentrated at the nodes is determined by the Maxwell-Mohr formula. The analytical estimate of the first frequency is calculated using the Dunkerley formula. The induction method is used to generalize a series of particular solutions for trusses with a consistently increasing number of panels. 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 rods by cutting out the nodes, are performed in the Maple computer mathematics system. Results. The frequency dependence on the number of panels for trusses with an arbitrary slope of the side faces is found in numerical form. An analytical solution can be obtained for the case of vertical faces of the structure when the truss has the shape of a regular triangular prism. A comparison of the analytical solution with the numerical one shows that the accuracy of the analytical estimate from below increases with an increase in the number of panels.