Formulas for calculating the deflection and natural frequency of vibrations of a planar arched truss

The object of research is a flat statically determinate arched truss with an arbitrary number of panels in the span. Formulas for the deflection and the first natural frequency of oscillations of the truss are derived. The equilibrium equations of the nodes are compiled and solved in the Maple computer mathematics system. Formulas are derived for the deflection of the middle node of the lower chord of the truss in the case of a uniform vertical load on the lower or upper chord. Method. A version of the Dunkerley method is used to calculate the natural frequency of oscillations of concentrated masses in the truss nodes. It is assumed that the masses oscillate vertically. Results. Good agreement is obtained between the results of the analytical solution and the numerical solution calculated considering all degrees of freedom of the system. It is shown that with an increase in the number of panels, the oscillation frequency decreases monotonically.